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Sum of the series 5+55+555+.. up to n terms

Find the sum up to n terms of the sequence: 5 + 55 + 555 + … up to n.
Examples :

Input : 2
Output: 60

Input : 3
Output: 595


Approach:The above problem can be solved using the following formula:

Sum = 5 + 55 + 555 + …. n terms.
= 5/9[9 + 99 + 999 + …. n terms]
= 5/9[(10 – 1) + (100 – 1) + (1000 – 1) + … n terms]
= 5/9[10 + 100 + 1000 ….. – (1 + 1 + … 1)]
= 5/9[10(10n – 1)/(10 – 1) + (1 + 1 + … n times))
= 50/81(10n – 1) – 5n/9

Below is the Implementation to find the sum of given series:

C++

// C++ program for sum of the 
// series 5 + 55 + 555.....n
#include <bits/stdc++.h>
using namespace std;
  
// function which return the
// the sum of series
int sumOfSeries(int n)
    return 0.6172 * 
           (pow(10, n) - 1) -
                    0.55 * n; 
      
}
  
// Driver code
int main()
{
    int n = 2; 
    cout << sumOfSeries(n);
    return 0;
}

Java

// Java program for sum of the 
// series 5 + 55 + 555.....n
  
class GFG 
{
  
    // function which return the
    // the sum of series
    static int sumOfSeries(int n)
    {
        return (int) (0.6172
                     (Math.pow(10, n) - 1) -
                                0.55 * n);
    }
      
    // Driver code
    public static void main(String []args)
    {
        int n = 2;
        System.out.println(sumOfSeries(n));
    }
}
  
// This code is contributed by UPENDRA BARTWAL.

Python3

# python program for sum of the 
# series 5 + 55 + 555.....n
  
def sumOfSeries(n):
    return (int) (0.6172 * 
                 (pow(10, n) - 1) -
                        0.55 * n)
  
  
# Driver Code
n = 2
print(sumOfSeries(n))
  
# This code is contributed 
# by Upendra Singh Bartwal

C#

// C# program for sum of the
// series 5 + 55 + 555.....n
using System;
  
class GFG 
{
  
    // Function which return the
    // the sum of series
    static int sumOfSeries(int n)
    {
        return (int)(0.6172 * 
                    (Math.Pow(10, n) - 1) -
                                 0.55 * n);
    }
      
    // Driver code
    public static void Main()
    {
        int n = 2;
        Console.Write(sumOfSeries(n));
    }
}
  
// This code is contributed by vt_m.

PHP

<?php
// PHP program for sum of the
//  series 5 + 55 + 555.....n
  
// function which return the
// the sum of series
function sumOfSeries($n)
    return (int)(0.6172 * 
                (pow(10, $n) - 1) - 
                        0.55 * $n);
}
  
// Driver code
$n = 2; 
echo(sumOfSeries($n));
  
// This code is contributed by Ajit.
?>


Output :

60


This article is attributed to GeeksforGeeks.org

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