求系列1+2+2+3+3+3+之和的程序N-yiteyi-C++库

给定一个正整数n，任务是求级数1+2+2+3+3+3的和，…+N 例如：

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Input : n = 5Output : 55   = 1 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 +      4 + 5 + 5 + 5 + 5 + 5.   = 55Input : n = 10Output : 385

推荐：请尝试你的方法 {IDE} 首先，在进入解决方案之前。

添加方法： 此外，该方法将所有元素逐一求和。下面是这种方法的实现。

C++

                         // Program to find                       
                         // sum of series                       
                         // 1 + 2 + 2 + 3 +                       
                         // . . . + n                       
                         #include <bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         // Function that find                       
                         // sum of series.                       
                         int                                     sumOfSeries(                                     int                                     n)                       
                         {                       
                                                 int                                     sum = 0;                       
                                                 for                                     (                                     int                                     i = 1; i <= n; i++)                       
                                                 for                                     (                                     int                                     j = 1; j <= i; j++)                       
                                                 sum = sum + i;                       
                                                 return                                     sum;                       
                         }                       
           
                         // Driver function                       
                         int                                     main()                       
                         {                       
                                                 int                                     n = 10;                       
           
                                                 // Function call                       
                                                 cout << sumOfSeries(n);                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java Program to                       
                         // find sum of                       
                         // series                       
                         // 1 + 2 + 2 + 3 +                       
                         // . . . + n                       
                         public                                     class                                     GfG{                       
           
                                                 // Function that find                       
                                                 // sum of series.                       
                                                 static                                     int                                     sumOfSeries(                                     int                                     n)                       
                                                 {                       
                                                 int                                     sum =                                     0                                     ;                       
                                   
                                                 for                                     (                                     int                                     i =                                     1                                     ; i <= n; i++)                       
                                                 for                                     (                                     int                                     j =                                     1                                     ; j <= i; j++)                       
                                                 sum = sum + i;                       
                                   
                                                 return                                     sum;                       
                                                 }                       
                                   
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     main(String s[])                       
                                                 {                       
                                                 int                                     n =                                     10                                     ;                       
                                                 System.out.println(sumOfSeries(n));                       
                                   
                                                 }                       
                         }                       
           
                         // This code is contributed by Gitanjali                       

Python3

                         # Python3 Program to                       
                         # find sum of series                       
                         # 1 + 2 + 2 + 3 +                       
                         # . . . + n                       
                         import                                     math                       
           
                         # Function that find                       
                         # sum of series.                       
                         def                                     sumOfSeries( n):                       
                                                 sum                                     =                                     0                       
                                                 for                                     i                                     in                                     range                                     (                                     1                                     , n                                     +                                     1                                     ):                       
                                                 sum                                     =                                     sum                                     +                                     i                                     *                                     i                       
                                                 return                                     sum                       
           
                         # Driver method                       
                         n                                     =                                     10                       
           
                         # Function call                       
                         print                                     (sumOfSeries(n))                       
           
                         # This code is contributed by Gitanjali                       

C#

                         // C# Program to find sum of                       
                         // series 1 + 2 + 2 + 3 + . . . + n                       
                         using                                     System;                       
           
                         public                                     class                                     GfG {                       
           
                                                 // Function that find                       
                                                 // sum of series.                       
                                                 static                                     int                                     sumOfSeries(                                     int                                     n)                       
                                                 {                       
                                                 int                                     sum = 0;                       
           
                                                 for                                     (                                     int                                     i = 1; i <= n; i++)                       
                                                 for                                     (                                     int                                     j = 1; j <= i; j++)                       
                                                 sum = sum + i;                       
           
                                                 return                                     sum;                       
                                                 }                       
           
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     Main()                       
                                                 {                       
                                                 int                                     n = 10;                       
                                                 Console.Write(sumOfSeries(n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed by vt_m.                       

PHP

                         <?php                       
                         // Program to find                       
                         // sum of series                       
                         // 1 + 2 + 2 + 3 +                       
                         // . . . + n                       
           
                         // Function that find                       
                         // sum of series.                       
                         function                                     sumOfSeries(                                     $n                                     )                       
                         {                       
                                                 $sum                                     = 0;                       
                                                 for                                     (                                     $i                                     = 1;                                     $i                                     <=                                     $n                                     ;                                     $i                                     ++)                       
                                                 for                                     (                                     $j                                     = 1;                                     $j                                     <=                                     $i                                     ;                                     $j                                     ++)                       
                                                 $sum                                     =                                     $sum                                     +                                     $i                                     ;                       
                                                 return                                     $sum                                     ;                       
                         }                       
           
                         // Driver Code                       
                         $n                                     = 10;                       
           
                         // Function call                       
                         echo                                     (sumOfSeries(                                     $n                                     ));                       
           
                         // This code is contributed by Ajit.                       
                         ?>                       

Javascript

                         <script>                       
                         // Javascript Program to                       
                         // find sum of                       
                         // series                       
                         // 1 + 2 + 2 + 3 +                       
                         // . . . + n                       
           
                                                 // Function that find                       
                                                 // sum of series.                       
                                                 function                                     sumOfSeries( n) {                       
                                                 let sum = 0;                       
           
                                                 for                                     (let i = 1; i <= n; i++)                       
                                                 for                                     (let j = 1; j <= i; j++)                       
                                                 sum = sum + i;                       
           
                                                 return                                     sum;                       
                                                 }                       
           
                                                 // Driver Code                       
                                                 let n = 10;                       
                                                 document.write(sumOfSeries(n));                       
           
           
                         // This code contributed by Princi Singh                       
           
                         </script>                       

输出：

时间复杂度：O（n） ^2. )

辅助空间： O（1） 乘法： 在乘法中，每一个元素都会自己相乘，然后相加。

   Input n = 10   sum = 1 + 2 + 2 + 3 + 3 + 3 + 4 + . . . + 10       = 1 + 2 * 2 + 3 * 3 + 4 * 4 + . . . + 10 * 10       = 1 + 4 + 9 + 16 + . . . + 100       = 385

C++

                         // Program to find                       
                         // sum of series                       
                         // 1 + 2 + 2 + 3 +                       
                         // . . . + n                       
                         #include <bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         // Function to find                       
                         // sum of series.                       
                         int                                     sumOfSeries(                                     int                                     n)                       
                         {                       
                                                 int                                     sum = 0;                       
                                                 for                                     (                                     int                                     i = 1; i <= n; i++)                       
                                                 sum = sum + i * i;                       
                                                 return                                     sum;                       
                         }                       
           
                         // Driver function.                       
                         int                                     main()                       
                         {                       
                                                 int                                     n = 10;                       
           
                                                 // Function call                       
                                                 cout << sumOfSeries(n);                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java Program to                       
                         // find sum of series                       
                         // 1 + 2 + 2 + 3 +                       
                         // . . . + n                       
                         public                                     class                                     GfG{                       
           
                                                 // Function that find sum of series.                       
                                                 static                                     int                                     sumOfSeries(                                     int                                     n)                       
                                                 {                       
                                                 int                                     sum =                                     0                                     ;                       
                                                 for                                     (                                     int                                     i =                                     1                                     ; i <= n; i++)                       
                                                 sum = sum + i * i;                       
                                                 return                                     sum;                       
                                                 }                       
           
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     main(String args[])                       
                                                 {                       
                                                 int                                     n =                                     10                                     ;                       
                                                 System.out.println(sumOfSeries(n));                       
                                   
                                                 }                       
                         }                       
           
                         // This code is contributed by Gitanjali                       

Python3

                         # Python3 Program to                       
                         # find sum of series                       
                         # 1 + 2 + 2 + 3 +                       
                         # . . . + n                       
                         import                                     math                       
           
                         # Function that find                       
                         # sum of series.                       
                         def                                     sumOfSeries( n):                       
                                                 sum                                     =                                     0                       
                                                 for                                     i                                     in                                     range                                     (                                     1                                     , n                                     +                                     1                                     ):                       
                                                 sum                                     =                                     sum                                     +                                     i                                     *                                     i                       
                                                 return                                     sum                       
           
                         # Driver method                       
                         n                                     =                                     10                       
                         # Function call                       
                         print                                     (sumOfSeries(n))                       
           
                         # This code is contributed by Gitanjali.                       

C#

                         // C# Program to find sum of series                       
                         // 1 + 2 + 2 + 3 + . . . + n                       
                         using                                     System;                       
           
                         class                                     GfG {                       
           
                                                 // Function that find sum of series.                       
                                                 static                                     int                                     sumOfSeries(                                     int                                     n)                       
                                                 {                       
                                                 int                                     sum = 0;                       
                                                 for                                     (                                     int                                     i = 1; i <= n; i++)                       
                                                 sum = sum + i * i;                       
                                                 return                                     sum;                       
                                                 }                       
           
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     Main()                       
                                                 {                       
                                                 int                                     n = 10;                       
                                                 Console.WriteLine(sumOfSeries(n));                       
                                   
                                                 }                       
                         }                       
           
                         // This code is contributed by anuj_67.                       

PHP

                         <?php                       
                         // Program to find                       
                         // sum of series                       
                         // 1 + 2 + 2 + 3 +                       
                         // . . . + n                       
           
                         // Function to find                       
                         // sum of series.                       
                         function                                     sumOfSeries(                                     $n                                     )                       
                         {                       
                                                 $sum                                     = 0;                       
                                                 for                                     (                                     $i                                     = 1;                                     $i                                     <=                                     $n                                     ;                                     $i                                     ++)                       
                                                 $sum                                     =                                     $sum                                     +                                     $i                                     *                                     $i                                     ;                       
                                                 return                                     $sum                                     ;                       
                         }                       
           
                         // Driver Code                       
                         $n                                     = 10;                       
           
                         // Function call                       
                         echo                                     (sumOfSeries(                                     $n                                     ));                       
           
                         // This code is contributed by Ajit.                       
                         ?>                       

Javascript

                         <script>                       
                         // javascript Program to                       
                         // find sum of series                       
                         // 1 + 2 + 2 + 3 +                       
                         // . . . + n                       
           
                                                 // Function that find sum of series.                       
                                                 function                                     sumOfSeries(n)                       
                                                 {                       
                                                 var                                     sum = 0;                       
                                                 for                                     (let i = 1; i <= n; i++)                       
                                                 sum = sum + i * i;                       
                                                 return                                     sum;                       
                                                 }                       
           
                                                 // Driver Code                       
                                                 var                                     n = 10;                       
                                                 document.write(sumOfSeries(n));                       
           
                         // This code is contributed by Amit Katiyar                       
                         </script>                       

输出：

时间复杂度：O（n）

辅助空间： O（1） 使用公式： 我们还使用公式来求级数之和。

    Input n = 10;   Sum of series = (n * (n + 1) * (2 * n + 1)) / 6    put n = 10 in the above formula    sum = (10 * (10 + 1) * (2 * 10 + 1)) / 6        = (10 * 11 * 21) / 6        = 385

C++

                         // C++ Program to                       
                         // find sum of series                       
                         // 1 + 2 + 2 + 3 +                       
                         // . . . + n                       
                         #include <bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         // Function to find                       
                         // sum of series.                       
                         int                                     sumOfSeries(                                     int                                     n)                       
                         {                       
                                                 return                                     (n * (n + 1) * (2 * n + 1)) / 6;                       
                         }                       
           
                         // Driver function                       
                         int                                     main()                       
                         {                       
                                                 int                                     n = 10;                       
           
                                                 // Function call                       
                                                 cout << sumOfSeries(n);                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java Program to                       
                         // find sum of series                       
                         // 1 + 2 + 2 + 3 +                       
                         // . . . + n                       
                         public                                     class                                     GfG                       
                         {                       
                                                 // Function that find                       
                                                 // sum of series.                       
                                                 static                                     int                                     sumOfSeries(                                     int                                     n)                       
                                                 {                       
                                                 return                                     (n * (n +                                     1                                     ) * (                                     2                                     * n +                                     1                                     )) /                                     6                                     ;                       
                                                 }                       
                                   
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     main(String s[])                       
                                                 {                       
                                                 int                                     n =                                     10                                     ;                       
                                                 System.out.println(sumOfSeries(n));                       
                                   
                                                 }                       
                         }                       
           
                         // This code is contributed by 'Gitanjali'.                       

Python3

                         # Python3 Program to                       
                         # find sum of series                       
                         # 1 + 2 + 2 + 3 +                       
                         # . . . + n                       
                         import                                     math                       
           
                         # Function that find                       
                         # sum of series.                       
                         def                                     sumOfSeries( n):                       
                                                 return                                     ((n                                     *                                     (n                                     +                                     1                                     )                                     *                                     (                                     2                                     *                                     n                                     +                                     1                                     ))                                     /                                     6                                     )                       
           
                         # Driver method                       
                         n                                     =                                     10                       
           
                         # Function call                       
                         print                                     (sumOfSeries(n))                       
           
                         # This code is contributed by Gitanjali                       

C#

                         // C# Program to find sum of series                       
                         // 1 + 2 + 2 + 3 + . . . + n                       
                         using                                     System;                       
           
                         public                                     class                                     GfG {                       
                                   
                                                 // Function that find                       
                                                 // sum of series.                       
                                                 static                                     int                                     sumOfSeries(                                     int                                     n)                       
                                                 {                       
                                                 return                                     (n * (n + 1) * (2 * n + 1)) / 6;                       
                                                 }                       
           
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     Main()                       
                                                 {                       
                                                 int                                     n = 10;                       
                                                 Console.WriteLine(sumOfSeries(n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed by 'vt_m'.                       

PHP

                         <?php                       
                         // PHP Program to                       
                         // find sum of series                       
                         // 1 + 2 + 2 + 3 +                       
                         // . . . + n                       
           
                         // Function to find                       
                         // sum of series.                       
                         function                                     sumOfSeries(                                     $n                                     )                       
                         {                       
                                                 return                                     (                                     $n                                     * (                                     $n                                     + 1) *                       
                                                 (2 *                                     $n                                     + 1)) / 6;                       
                         }                       
           
                         // Driver Code                       
                         $n                                     = 10;                       
           
                         // Function call                       
                         echo                                     (sumOfSeries(                                     $n                                     ));                       
           
                         // This code is contributed by Ajit.                       
                         ?>                       

Javascript

                         <script>                       
                         // javascript Program to                       
                         // find sum of series                       
                         // 1 + 2 + 2 + 3 +                       
                         // . . . + n                       
           
                         // Function that find                       
                         // sum of series.                       
                         function                                     sumOfSeries(n)                       
                         {                       
                                                 return                                     (n * (n + 1) * (2 * n + 1)) / 6;                       
                         }                       
           
                         // Driver Code                       
                         var                                     n = 10;                       
                         document.write(sumOfSeries(n));                       
           
           
                         // This code is contributed by Amit Katiyar                       
                         </script>                       

输出：

时间复杂度：O（1）

辅助空间：O（1）请参考自然数平方和有关上述公式和更多优化的详细信息。

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