# 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `// 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 ` `    ``// 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 ` `# 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 ` `    ``// 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

 ` `

Output :

```1.46286
```

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