# Sum of the series 0.7, 0.77, 0.777, … upto n terms

Given n the number of terms. Find the sum of the series 0.7, 0.77, 0.777, … upto n terms.
Examples :

```Input : 2
Output : 1.46286

Input : 3
Output : 2.23609```

Approach Used :
Let’s denote the sum of the series by S:

Sum = 0.7 + 0.77 + 0.777 + …. up to n terms
= 7/9(0.9 + 0.99 + 0.999 + … up to n terms)
= 7/9[(1 – 0.1) + (1 – 0.01) + (1-0.001) + … up to n terms]
= 7/9[(1 + 1 + 1… upto n terms) – (1/10 + 1/100 + 1/1000 + … upto n terms)]
= 7/9[n – 0.1 * (1 – (0.1)n)/(1 – 0.1)]
= 7/81[9n – 1 + 10-n

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

## C++

 `// C++ program for sum of the series 0.7,  ``// 0.77, 0.777, ... upto n terms ``#include ``using` `namespace` `std; `` ` `// function which return  ``// the sum of series ``float` `sumOfSeries(``int` `n) ``{ ``    ``return` `.086 * (9 * n - 1 + ``           ``pow``(10, (-1) * n)); ``} `` ` `// Driver code ``int` `main() ``{ ``    ``int` `n = 2; ``    ``cout << sumOfSeries(n); ``    ``return` `0; ``} `

## Java

 `// Java program for sum of the series 0.7,  ``// 0.77, 0.777, ... upto n terms ``import` `java.io.*; ``import` `java.math.*; `` ` `class` `GFG { `` ` `    ``// function which return  ``    ``// the sum of series ``    ``static` `float` `sumOfSeries(``int` `n) ``    ``{ ``        ``return` `.086f * (``9` `* n - ``1` `+  ``        ``(``float``)(Math.pow(``10``, (-``1``) * n))); ``    ``} `` ` `    ``// Driver code ``    ``public` `static` `void` `main(String args[]) ``    ``{ ``        ``int` `n = ``2``; ``        ``System.out.println(sumOfSeries(n)); ``    ``} ``} `` ` `/*This code is contributed by Nikita Tiwari.*/`

## Python3

 `# Python 3 program for sum of the series 0.7,  ``# 0.77, 0.777, ... upto n terms ``import` `math `` ` `# Function which return  ``# the sum of series ``def` `sumOfSeries(n) : ``    ``return` `.``086` `*` `(``9` `*` `n ``-` `1` `+` `math.``pow``(``10``, (``-``1``) ``*` `n)); `` ` ` ` `# Driver code ``n ``=` `2``print``(sumOfSeries(n)) `` ` ` ` `# This code is contributed by Nikita Tiwari. `

## C#

 `// C# program for sum of the series   ``// 0.7, 0.77, 0.777, ... upto n terms ``using` `System; `` ` `class` `GFG { `` ` `    ``// Function which return  ``    ``// the sum of series ``    ``static` `float` `sumOfSeries(``int` `n) ``    ``{ ``        ``return` `.086f * (9 * n - 1 +  ``               ``(``float``)(Math.Pow(10, (-1) * n))); ``    ``} `` ` `    ``// Driver code ``    ``public` `static` `void` `Main() ``    ``{ ``        ``int` `n = 2; ``        ``Console.Write(sumOfSeries(n)); ``    ``} ``} `` ` `// This code is contributed by vt_m. `

## PHP

 ` `

## Javascript

 ` `

Output:

`1.46286`

Time Complexity: O(logn), where n is the given integer.

Auxiliary Space: O(1), no extra space is required, so it is a constant.

Previous
Next