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

• Difficulty Level : Medium
• Last Updated : 23 Jun, 2022

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

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## Javascript

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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.

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