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Sum of the sequence 2, 22, 222, ………

  • Difficulty Level : Medium
  • Last Updated : 12 Apr, 2021

Find the sum of the following sequence : 2, 22, 222, ……… to n terms. 
Examples : 
 

Input : 2
Output: 1.9926

Input : 3
Output: 23.9112

 

A simple solution is to compute terms one by one and add to the result.
The above problem can be efficiently solved using the following formula:
 

 



C++




// CPP program to find sum of series
// 2, 22, 222, ..
#include <bits/stdc++.h>
using namespace std;
 
// function which return the
// the sum of series
float sumOfSeries(int n)
{
    return 0.0246 * (pow(10, n) - 1 - (9 * n));
}
 
// driver code
int main()
{
    int n = 3;
    cout << sumOfSeries(n);
    return 0;
}

Java




// JAVA Code for Sum of the
// sequence 2, 22, 222,...
import java.util.*;
 
class GFG {
     
    // function which return the
    // the sum of series
    static double sumOfSeries(int n)
    {
        return 0.0246 * (Math.pow(10, n)
                            - 1 - (9 * n));
    }
     
    /* Driver program */
    public static void main(String[] args)
    {
         int n = 3;
         System.out.println(sumOfSeries(n));
    }
}
 
// This code is contributed by Arnav Kr. Mandal.

Python3




# Python3 code to find
# sum of series
# 2, 22, 222, ..
import math
 
# function which return
# the sum of series
def sumOfSeries( n ):
    return 0.0246 * (math.pow(10, n) - 1 - (9 * n))
     
# driver code
n = 3
print( sumOfSeries(n))
 
# This code is contributed by "Sharad_Bhardwaj".

C#




// C# Code for Sum of the
// sequence 2, 22, 222,...
using System;
 
class GFG {
     
    // Function which return the
    // the sum of series
    static double sumOfSeries(int n)
    {
        return 0.0246 * (Math.Pow(10, n)
                           - 1 - (9 * n));
    }
     
    // Driver Code
    public static void Main()
    {
        int n = 3;
        Console.Write(sumOfSeries(n));
    }
}
 
// This code is contributed by vt_m.

PHP




<?php
// PHP program to find sum
// of series 2, 22, 222, ..
 
// function which return the
// the sum of series
function sumOfSeries($n)
{
    return 0.0246 * (pow(10, $n) -
                     1 - (9 * $n));
}
 
// Driver Code
$n = 3;
echo(sumOfSeries($n));
 
// This code is contributed by Ajit.
?>

Javascript




<script>
 
// JavaScript program for Sum of the
// sequence 2, 22, 222,...
 
    // function which return the
    // the sum of series
    function sumOfSeries(n)
    {
        return 0.0246 * (Math.pow(10, n)
                            - 1 - (9 * n));
    }
 
// Driver code   
          
        let n = 3;
        document.write(sumOfSeries(n));
             
</script>

Output : 

23.9112

 

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