求系列1+11+111+1111+的和…。。最多n个术语-yiteyi-C++库

在这里，我们将找到系列1+11+111+1111+的和…。。最多N个术语（其中N是给定的）。 例子：

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Input : 3Output : 1 + 11 + 111 +....Total sum is : 123Input : 4Output : 1 + 11 + 111 + 1111 +..... Total sum is : 1234Input : 7Output : 1 + 11 + 111 + 1111 + 11111 +          111111 + 1111111 +..... Total sum is : 1234567

推荐：请尝试你的方法 {IDE} 首先，在进入解决方案之前。

这里我们看到，当N的值为3时，级数持续到1+11+111，即三项，其和为123。求上述级数之和的程序：

C++

                         // C++ program to find the sum of                       
                         // the series 1+11+111+1111+....                       
                         #include <bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         // Function for finding summation                       
                         int                                     summation(                                     int                                     n)                       
                         {                       
                                                 int                                     sum = 0, j = 1;                       
                                                 for                                     (                                     int                                     i = 1; i <= n; i++) {                       
                                                 sum = sum + j;                       
           
                                                 // Appending a 1 at the end                       
                                                 j = (j * 10) + 1;                       
                                                 }                       
           
                                                 return                                     sum;                       
                         }                       
           
                         // Driver Code                       
                         int                                     main()                       
                         {                       
                                                 int                                     n = 5;                       
                                                 cout <<                                     " "                                     <<  summation(n);                       
                                                 return                                     0;                       
                         }                       
           
                         // This code is contributed by shivanisinghss2110                       

C

                         // C program to find the sum of                       
                         // the series 1+11+111+1111+....                       
                         #include <stdio.h>                       
           
                         // Function for finding summation                       
                         int                                     summation(                                     int                                     n)                       
                         {                       
                                                 int                                     sum = 0, j = 1;                       
                                                 for                                     (                                     int                                     i = 1; i <= n; i++) {                       
                                                 sum = sum + j;                       
           
                                                 // Appending a 1 at the end                       
                                                 j = (j * 10) + 1;                       
                                                 }                       
           
                                                 return                                     sum;                       
                         }                       
           
                         // Driver Code                       
                         int                                     main()                       
                         {                       
                                                 int                                     n = 5;                       
                                                 printf                                     (                                     "%d"                                     , summation(n));                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java program to find the sum of                       
                         // the series 1+11+111+1111+....                       
                         import                                     java.io.*;                       
           
                         class                                     GFG                       
                         {                       
           
                                                 // Function for finding summation                       
                                                 static                                     int                                     summation(                                     int                                     n)                       
                                                 {                       
                                                 int                                     sum =                                     0                                     , j =                                     1                                     ;                       
                                                 for                                     (                                     int                                     i =                                     1                                     ; i <= n; i++)                       
                                                 {                       
                                                 sum = sum + j;                       
                                                 j = (j *                                     10                                     ) +                                     1                                     ;                       
                                                 }                       
           
                                                 return                                     sum;                       
                                                 }                       
           
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     main(String args[])                       
                                                 {                       
                                                 int                                     n =                                     5                                     ;                       
                                                 System.out.println(summation(n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed                       
                         // by Nikita Tiwari                       

python

                         # Python program to get the summation                       
                         # of following series                       
                         def                                     summation(n):                       
                                                 sum                                     =                                     0                       
                                                 j                                     =                                     1                       
                                   
                                                 for                                     i                                     in                                     range                                     (                                     1                                     , n                                     +                                     1                                     ):                       
                                                 sum                                     =                                     sum                                     +                                     j                       
                                                 j                                     =                                     (j                                     *                                     10                                     )                                     +                                     1                       
                                   
                                                 return                                     sum                       
                                   
                         # Driver Code                       
                         n                                     =                                     5                       
                         print                                     (summation(n))                       

C#

                         // C# program to find the sum of                       
                         // the series 1+11+111+1111+....                       
                         using                                     System;                       
           
                         class                                     GFG                       
                         {                       
           
                                                 // Function for finding summation                       
                                                 static                                     int                                     summation(                                     int                                     n)                       
                                                 {                       
                                                 int                                     sum = 0, j = 1;                       
                                                 for                                     (                                     int                                     i = 1; i <= n; i++)                       
                                                 {                       
                                                 sum = sum + j;                       
                                                 j = (j * 10) + 1;                       
                                                 }                       
           
                                                 return                                     sum;                       
                                                 }                       
           
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     Main()                       
                                                 {                       
                                                 int                                     n = 5;                       
                                                 Console.WriteLine(summation(n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed by vt_m                       

PHP

                         <?php                       
                         // PHP program to find the sum of                       
                         // the series 1+11+111+1111+....                       
           
                         // Function for finding summation                       
                         function                                     summation(                                     $n                                     )                       
                         {                       
                                                 $sum                                     = 0;                                     $j                                     = 1;                       
                                                 for                                     (                                     $i                                     = 1;                                     $i                                     <=                                     $n                                     ;                                     $i                                     ++)                       
                                                 {                       
                                                 $sum                                     =                                     $sum                                     +                                     $j                                     ;                       
           
                                                 // Appending a 1 at the end                       
                                                 $j                                     = (                                     $j                                     * 10) + 1;                       
                                                 }                       
           
                                                 return                                     $sum                                     ;                       
                         }                       
           
                         // Driver Code                       
                         $n                                     = 5;                       
                         echo                                     summation(                                     $n                                     );                       
           
                         // This code is contributed by ajit                       
                         ?>                       

Javascript

                         <script>                       
           
                         // Javascript program to find the sum of                       
                         // the series 1+11+111+1111+....                       
           
                                                 // Function for finding summation                       
                                                 function                                     summation( n) {                       
                                                 let sum = 0, j = 1;                       
                                                 for                                     ( let i = 1; i <= n; i++) {                       
                                                 sum = sum + j;                       
                                   
                                                 // Appending a 1 at the end                       
                                                 j = (j * 10) + 1;                       
                                                 }                       
           
                                                 return                                     sum;                       
                                                 }                       
           
                                                 // Driver Code                       
                                   
                                                 let n = 5;                       
                                                 document.write(summation(n));                       
                                   
                         // This code contributed by Princi Singh                       
           
                         </script>                       

输出：

另一种方法： 设一系列S=1+11+111+1111+…+直到第n学期。用公式求级数之和。

$\ S = 1 + 11 + 111 + 1111 + . . . + upto n term \ \ S = left ( frac{1}{9} ight )*left ( 9 + 99 + 999 + 9999 + . . . + upto n term ight ) \ \ S = left ( frac{1}{9} ight ) * left ( left (10 ^{1} - 1 ight ) + left (10 ^{2} -1 ight ) +left (10 ^{3} -1 ight ) + left (10 ^{4} -1 ight ) + . . . + left (10 ^{n} -1 ight ) ight ) \ \ S = left ( frac{1}{9} ight ) *left (10 ^{1} + 10 ^{2} + 10 ^{3} + 10 ^{4} + . . . + 10 ^{n} - n ight ) \ \ S = left ( frac{1}{9} ight ) * left ( frac{10 * (10^{n} - 1)}{10 - 1} - n ight ) \ \ S = frac{10^{n+1} - 10 - 9n}{81}$

下面是上述方法的实现。

C++

                         // C++ program to find the sum of                       
                         // the series 1+11+111+1111+....                       
                         #include <bits/stdc++.h>                       
           
                         // Function for finding summation                       
                         int                                     summation(                                     int                                     n)                       
                         {                       
                                                 int                                     sum;                       
           
                                                 sum = (                                     pow                                     (10, n + 1) -                       
                                                 10 - (9 * n)) / 81;                       
           
                                                 return                                     sum;                       
                         }                       
           
                         // Driver Code                       
                         int                                     main()                       
                         {                       
                                                 int                                     n = 5;                       
                                                 printf                                     (                                     "%d"                                     , summation(n));                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // java program to find the sum of                       
                         // the series 1+11+111+1111+....                       
                         import                                     java.io.*;                       
           
                         class                                     GFG {                       
           
                                                 // Function for finding summation                       
                                                 static                                     int                                     summation(                                     int                                     n)                       
                                                 {                       
                                                 int                                     sum;                       
                                   
                                                 sum = (                                     int                                     )(Math.pow(                                     10                                     , n +                                     1                                     ) -                       
                                                 10                                     - (                                     9                                     * n)) /                                     81                                     ;                       
                                   
                                                 return                                     sum;                       
                                                 }                       
                                   
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     main (String[] args)                       
                                                 {                       
                                                 int                                     n =                                     5                                     ;                       
                                                 System.out.println(summation(n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed by anuj_67.                       

Python3

                         # Python3 program to                       
                         # find the sum of                       
                         # the series 1+11+111+1111+....                       
                         import                                     math                       
           
                         # Function for                       
                         # finding summation                       
                         def                                     summation(n):                       
                                                 return                                     int                                     ((                                     pow                                     (                                     10                                     , n                                     +                                     1                                     )                                     -                       
                                                 10                                     -                                     (                                     9                                     *                                     n))                                     /                                     81                                     );                       
           
                         # Driver Code                       
                         print                                     (summation(                                     5                                     ));                       
           
                         # This code is contributed                       
                         # by mits.                       

C#

                         // C# program to find the sum of                       
                         // the series 1+11+111+1111+....                       
                         using                                     System;                       
           
                         class                                     GFG {                       
           
                                                 // Function for finding summation                       
                                                 static                                     int                                     summation(                                     int                                     n)                       
                                                 {                       
                                                 int                                     sum;                       
                                   
                                                 sum = (                                     int                                     )(Math.Pow(10, n + 1) -                       
                                                 10 - (9 * n)) / 81;                       
                                   
                                                 return                                     sum;                       
                                                 }                       
                                   
                                                 // Driver Code                       
                                                 public                                     static                                     void                                     Main ()                       
                                                 {                       
                                                 int                                     n = 5;                       
                                                 Console.WriteLine(summation(n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed by anuj_67.                       

PHP

                         <?php                       
                         //PHP program to find the sum of                       
                         // the series 1+11+111+1111+....                       
           
                         // Function for finding summation                       
                         function                                     summation(                                     $n                                     )                       
                         {                       
                                                 $sum                                     ;                       
           
                                                 $sum                                     = (pow(10,                                     $n                                     + 1) -                       
                                                 10 - (9 *                                     $n                                     )) / 81;                       
           
                                                 return                                     $sum                                     ;                       
                         }                       
           
                         // Driver Code                       
                         $n                                     = 5;                       
                         echo                                     summation(                                     $n                                     );                       
           
                         // This code is contributed by aj_36                       
                         ?>                       

Javascript

                         <script>                       
                         // javascript program to find the sum of                       
                         // the series 1+11+111+1111+....                       
           
                         // Function for finding summation                       
                         function                                     summation( n)                       
                         {                       
                                                 let sum;                       
                                                 sum = (Math.pow(10, n + 1) -                       
                                                 10 - (9 * n)) / 81;                       
                                                 return                                     sum;                       
                         }                       
           
                         // Driver Code                       
                         let n = 5;                       
                                                 document.write(summation(n)) ;                       
                                   
                         // This code is contributed by aashish1995                       
           
                         </script>                       

输出：

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