系列1、17、98、354的第n项……-yiteyi-C++库

给出一个系列1，17，98，354……找出这个系列的第n项。级数基本上代表前n个自然数的四次方之和。第一项是1的和 ^4. .第二项是两个数字的总和，即（1 ^4. + 2 ^4. =17），第三项，即（1） ^4. + 2 ^4. + 3 ^4. ）等等。

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例如：

Input : 5Output : 979Input : 7Output : 4676

推荐：请尝试你的方法 {IDE} 首先，在进入解决方案之前。

天真的方法： 一个简单的解决方案是将前n个自然数的四次方相加。通过迭代，我们可以很容易地找到级数的第n项。以下是上述方法的实施情况：

C++

                         // CPP program to find n-th term of                       
                         // series                       
                         #include <iostream>                       
                         using                                     namespace                                     std;                       
           
                         // Function to find the nth term of series                       
                         int                                     sumOfSeries(                                     int                                     n)                       
                         {                       
                                                 // Loop to add 4th powers                       
                                                 int                                     ans = 0;                       
                                                 for                                     (                                     int                                     i = 1; i <= n; i++)                       
                                                 ans += i * i * i * i;                       
           
                                                 return                                     ans;                       
                         }                       
           
                         // Driver code                       
                         int                                     main()                       
                         {                       
                                                 int                                     n = 4;                       
                                                 cout << sumOfSeries(n);                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java program to find n-th term of                       
                         // series                       
                         import                                     java.io.*;                       
           
                         class                                     GFG {                       
           
                                                 // Function to find the nth term of series                       
                                                 static                                     int                                     sumOfSeries(                                     int                                     n)                       
                                                 {                       
                                                 // Loop to add 4th powers                       
                                                 int                                     ans =                                     0                                     ;                       
                                                 for                                     (                                     int                                     i =                                     1                                     ; i <= n; i++)                       
                                                 ans += i * i * i * i;                       
           
                                                 return                                     ans;                       
                                                 }                       
           
                                                 // Driver code                       
                                                 public                                     static                                     void                                     main(String args[])                       
                                                 {                       
                                                 int                                     n =                                     4                                     ;                       
                                                 System.out.println(sumOfSeries(n));                       
                                                 }                       
                         }                       

Python3

                         # Python 3 program to find                       
                         # n-th term of                       
                         # series                       
                                   
                                   
                         # Function to find the                       
                         # nth term of series                       
                         def                                     sumOfSeries(n) :                       
                                                 # Loop to add 4th powers                       
                                                 ans                                     =                                     0                       
                                                 for                                     i                                     in                                     range                                     (                                     1                                     , n                                     +                                     1                                     ) :                       
                                                 ans                                     =                                     ans                                     +                                     i                                     *                                     i                                     *                                     i                                     *                                     i                       
                                   
                                                 return                                     ans                       
                                   
                                   
                         # Driver code                       
                         n                                     =                                     4                       
                         print                                     (sumOfSeries(n))                       

C#

                         // C# program to find n-th term of                       
                         // series                       
                         using                                     System;                       
                         class                                     GFG {                       
           
                                                 // Function to find the                       
                                                 // nth term of series                       
                                                 static                                     int                                     sumOfSeries(                                     int                                     n)                       
                                                 {                       
                                   
                                                 // Loop to add 4th powers                       
                                                 int                                     ans = 0;                       
                                                 for                                     (                                     int                                     i = 1; i <= n; i++)                       
                                                 ans += i * i * i * i;                       
           
                                                 return                                     ans;                       
                                                 }                       
           
                                                 // Driver code                       
                                                 public                                     static                                     void                                     Main()                       
                                                 {                       
                                                 int                                     n = 4;                       
                                                 Console.WriteLine(sumOfSeries(n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed by anuj_67                       

PHP

                         <?php                       
                         // PHP program to find                       
                         // n-th term of series                       
           
                         // Function to find the                       
                         // nth term of series                       
                         function                                     sumOfSeries(                                     $n                                     )                       
                         {                       
                                                 // Loop to add 4th powers                       
                                                 $ans                                     = 0;                       
                                                 for                                     (                                     $i                                     = 1;                                     $i                                     <=                                     $n                                     ;                                     $i                                     ++)                       
                                                 $ans                                     +=                                     $i                                     *                                     $i                                     *                                     $i                                     *                                     $i                                     ;                       
           
                                                 return                                     $ans                                     ;                       
                         }                       
           
                         // Driver code                       
                         $n                                     = 4;                       
                         echo                                     sumOfSeries(                                     $n                                     );                       
           
                         // This code is contributed                       
                         // by anuj_67                       
                         ?>                       

Javascript

                         <script>                       
           
                         // Javascript program to find n-th term of                       
                         // series                       
           
           
                         // Function to find the nth term of series                       
                         function                                     sumOfSeries( n)                       
                         {                       
                                                 // Loop to add 4th powers                       
                                                 let ans = 0;                       
                                                 for                                     (let i = 1; i <= n; i++)                       
                                                 ans += i * i * i * i;                       
           
                                                 return                                     ans;                       
                         }                       
           
           
                         // Driver Code                       
           
                         let n = 4;                       
                         document.write(sumOfSeries(n));                       
           
           
                         </script>                       

输出：

时间复杂性： O（n）。

有效方法： 本系列中的模式是n项等于 第（n-1）项与第n项之和 ^4. .

例如：

n = 22nd term equals to sum of 1st term and 2⁴ i.e 16A2 = A1 + 16    = 1 + 16   = 17Similarly,A3 = A2 + 3⁴   = 17 + 81   = 98 and so on..

我们得到：

A(n) = A(n - 1) + n⁴      = A(n - 2) + n⁴  + (n-1)⁴      = A(n - 3) + n⁴  + (n-1)⁴ + (n-2)⁴       .       .       .     = A(1) + 16 + 81... + (n-1)⁴ + n⁴A(n) = 1 + 16 + 81 +... + (n-1)⁴ + n⁴     = n(n + 1)(6n^{3 + 9n2 + n - 1) / 30}i.e A(n) is sum of 4th powers of First n natural numbers.

以下是上述方法的实施情况：

C++

                         // CPP program to find the n-th                       
                         // term in series                       
                         #include <bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         // Function to find nth term                       
                         int                                     sumOfSeries(                                     int                                     n)                       
                         {                       
                                                 return                                     n * (n + 1) * (6 * n * n * n                       
                                                 + 9 * n * n + n - 1) / 30;                       
                         }                       
           
                         // Driver code                       
                         int                                     main()                       
                         {                       
                                                 int                                     n = 4;                       
                                                 cout << sumOfSeries(n);                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java program to find the n-th                       
                         // term in series                       
                         import                                     java.io.*;                       
           
                         class                                     Series {                       
           
                                                 // Function to find nth term                       
                                                 static                                     int                                     sumOfSeries(                                     int                                     n)                       
                                                 {                       
                                                 return                                     n * (n +                                     1                                     ) * (                                     6                                     * n * n * n                       
                                                 +                                     9                                     * n * n + n -                                     1                                     ) /                                     30                                     ;                       
                                                 }                       
           
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     main(String[] args)                       
                                                 {                       
                                                 int                                     n =                                     4                                     ;                       
                                                 System.out.println(sumOfSeries(n));                       
                                                 }                       
                         }                       

python

                         # Python program to find the Nth                       
                         # term in series                       
                                   
                         # Function to print nth term                       
                         # of series                       
                         def                                     sumOfSeries(n):                       
                                                 return                                     n                                     *                                     (n                                     +                                     1                                     )                                     *                                     (                                     6                                     *                                     n                                     *                                     n                                     *                                     n                       
                                                 +                                     9                                     *                                     n                                     *                                     n                                     +                                     n                                     -                                     1                                     )                                     /                                     30                       
                                   
                         # Driver code                       
                         n                                     =                                     4                       
                         print                                     sumOfSeries(n)                       

C#

                         // C# program to find the n-th                       
                         // term in series                       
                         using                                     System;                       
                         class                                     Series {                       
           
                                                 // Function to find nth term                       
                                                 static                                     int                                     sumOfSeries(                                     int                                     n)                       
                                                 {                       
                                                 return                                     n * (n + 1) * (6 * n * n * n                       
                                                 + 9 * n * n + n - 1) / 30;                       
                                                 }                       
           
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     Main()                       
                                                 {                       
                                                 int                                     n = 4;                       
                                                 Console.WriteLine(sumOfSeries(n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed by anuj_67                       

PHP

                         <?php                       
                         // PHP program to find the n-th                       
                         // term in series                       
           
                         // Function to find nth term                       
                         function                                     sumOfSeries(                                     $n                                     )                       
                         {                       
                                                 return                                     $n                                     * (                                     $n                                     + 1) * (6 *                                     $n                                     *                                     $n                                     *                       
                                                 $n                                     + 9 *                                     $n                                     *                                     $n                                     +                                     $n                                     - 1) / 30;                       
                         }                       
           
                                                 // Driver code                       
                                                 $n                                     = 4;                       
                                                 echo                                     sumOfSeries(                                     $n                                     );                       
           
                         // This code is contributed by anuj_67                       
                         ?>                       

Javascript

                         <script>                       
                                                 // Javascript program to find the n-th term in series                       
                                   
                                                 // Function to find nth term                       
                                                 function                                     sumOfSeries(n)                       
                                                 {                       
                                                 return                                     n * (n + 1) * (6 * n * n * n + 9 * n * n + n - 1) / 30;                       
                                                 }                       
                                   
                                                 let n = 4;                       
                                                 document.write(sumOfSeries(n));                       
           
                         // This code is contributed by divyeshrabadiya07.                       
                         </script>                       

输出：

时间复杂性： O（1）。

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