Find the sum of the series 1+11+111+1111+….. upto n terms

• Last Updated : 24 Mar, 2021

Here we are going to find the sum of the series 1 + 11 + 111 + 1111 +…..upto N terms (where N is given).
Example :

Input : 3
Output : 1 + 11 + 111 +....
Total sum is : 123

Input : 4
Output : 1 + 11 + 111 + 1111 +.....
Total sum is : 1234

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

Here we see that when value of N is 3, series last upto 1 + 11 + 111 i.e, three term and it’s sum is 123.
Program for finding sum of above series :

C++

 // C++ program to find the sum of// the series 1+11+111+1111+....#include using namespace std; // Function for finding summationint 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 Codeint 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  // Function for finding summationint 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 Codeint 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 seriesdef summation(n):    sum = 0    j = 1         for i in range(1, n + 1):        sum = sum + j        j = (j * 10) + 1             return sum         # Driver Coden = 5print(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



Javascript



Output :

12345

Another method: Let given a series S = 1 + 11 + 111 + 1111 + . . . + upto nth term. Using formula to find sum of series. Below is the implementation of above approach.

C++

 // C++ program to find the sum of// the series 1+11+111+1111+....#include  // Function for finding summationint summation(int n){    int sum;     sum = (pow(10, n + 1) -               10 - (9 * n)) / 81;     return sum;} // Driver Codeint 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 summationdef summation(n):    return int((pow(10, n + 1) -                    10 - (9 * n)) / 81); # Driver Codeprint(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.



Javascript



Output :

12345

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