# Find geometric sum of the series using recursion

• Difficulty Level : Easy
• Last Updated : 09 Aug, 2021

Given an integer N, we need to find the geometric sum of the following series using recursion.

1 + 1/3 + 1/9 + 1/27 + … + 1/(3^n)

Examples:

```Input N = 5
Output: 1.49794

Input: N = 7
Output: 1.49977```

Approach:
In the above-mentioned problem, we are asked to use recursion. We will calculate the last term and call recursion on the remaining n-1 terms each time. The final sum returned is the result.
Below is the implementation of the above approach:

## C++

 `// CPP implementation to Find the``// geometric sum of the series using recursion` `#include ``using` `namespace` `std;` `// function to find the sum of given series``double` `sum(``int` `n)``{``    ``// base case``    ``if` `(n == 0)``        ``return` `1;` `    ``// calculate the sum each time``    ``double` `ans = 1 / (``double``)``pow``(3, n) + sum(n - 1);` `    ``// return final answer``    ``return` `ans;``}` `// Driver code``int` `main()``{` `    ``// integer initialisation``    ``int` `n = 5;` `    ``cout << sum(n) << endl;` `    ``return` `0;``}`

## Java

 `// JAVA implementation to Find the``// geometric sum of the series using recursion` `import` `java.util.*;` `class` `GFG {` `    ``static` `double` `sum(``int` `n)``    ``{``        ``// base case``        ``if` `(n == ``0``)``            ``return` `1``;` `        ``// calculate the sum each time``        ``double` `ans = ``1` `/ (``double``)Math.pow(``3``, n) + sum(n - ``1``);` `        ``// return final answer``        ``return` `ans;``    ``}` `    ``// Driver code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``// integer initialisation``        ``int` `n = ``5``;` `        ``// print result``        ``System.out.println(sum(n));``    ``}``}`

## Python3

 `# CPP implementation to Find the``# geometric sum of the series using recursion`  `def` `sum``(n):``    ` `    ``# base case``    ``if` `n ``=``=` `0``:``        ``return` `1``    ` `    ``# calculate the sum each time``    ``# and return final answer``    ``return` `1` `/` `pow``(``3``, n) ``+` `sum``(n``-``1``)` `n ``=` `5``;` `print``(``sum``(n));`

## C#

 `// C# implementation to Find the``// geometric sum of the series using recursion` `using` `System;` `class` `GFG {` `    ``static` `double` `sum(``int` `n)``    ``{``        ``// base case``        ``if` `(n == 0)``            ``return` `1;` `        ``// calculate the sum each time``        ``double` `ans = 1 / (``double``)Math.Pow(3, n) + sum(n - 1);` `        ``// return final answer``        ``return` `ans;``    ``}` `    ``// Driver code``    ``static` `public` `void` `Main()``    ``{``        ``int` `n = 5;` `        ``Console.WriteLine(sum(n));``    ``}``}`

## Javascript

 ``
Output:
`1.49794`

Time Complexity: O(N)
Auxiliary Space: O(N)

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