Find geometric sum of the series using recursion Last Updated : 15 Mar, 2025 Comments Improve Suggest changes Like Article Like Report 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/(3n) Examples: Input: n = 5 Output: 1.49794Explanation: 1 + 1/3 + 1/9 + 1/27 + 1/81 + 1/243 = 1.49794Input: n = 7Output: 1.49977Approach:To find the geometric sum of the series 1 + 1/3 + 1/3² + ... + 1/3ⁿ. The base case returns 1 when n = 0. For each recursive call, the function adds 1/3ⁿ to the sum of the remaining terms. The recursion continues until n reaches 0, ensuring all terms are added. C++ // CPP implementation to Find the // geometric sum of the series using recursion #include <bits/stdc++.h> 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 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)); } } Python 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# 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 function sum(n) { // base case if (n == 0) return 1; // calculate the sum each time var ans = 1 / Math.pow(3, n) + sum(n - 1); // return final answer return ans; } // Driver code // integer initialisation var n = 5; console.log(sum(n).toFixed(5)); Output1.49794Time Complexity: O(n)Auxiliary Space: O(n), due to recursive function calls stored in the call stack. Comment More infoAdvertise with us Next Article Find geometric sum of the series using recursion M mv15 Follow Improve Article Tags : Algorithms Recursion DSA Practice Tags : AlgorithmsRecursion Similar Reads Introduction to Recursion The process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution 14 min read What is Recursion? Recursion is defined as a process which calls itself directly or indirectly and the corresponding function is called a recursive function.Example 1 : Sum of Natural Numbers Let us consider a problem to find the sum of natural numbers, there are several ways of doing that but the simplest approach is 8 min read Difference between Recursion and Iteration A program is called recursive when an entity calls itself. 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