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++

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// 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;
}

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Java














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// 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. 



















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Python3














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# 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 



















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C#














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// 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. 



















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PHP














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<?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. 


?> 



















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Output :


60





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