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.
?>

Javascript

<script>
// javascript program for sum of the
// series 5 + 55 + 555.....n

    // function which return the
    // the sum of series
    function sumOfSeries(n) {
        return parseInt( (0.6172 * (Math.pow(10, n) - 1) - 0.55 * n));
    }

    // Driver code
    var n = 2;
    document.write(sumOfSeries(n));

// This code is contributed by aashish1995
</script>

Output :

60

Time complexity: O(log n) since using the inbuilt power function.

Auxiliary Space:  O(1)