# Find geometric sum of the series using recursion

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)

Feeling lost in the world of random DSA topics, wasting time without progress? It's time for a change! Join our DSA course, where we'll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 geeks!

Previous
Next