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Sum of the sequence 2, 22, 222, ………
  • Difficulty Level : Medium
  • Last Updated : 25 Apr, 2018

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.
?>


Output :

23.9112

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