Given two integers A and R, representing the first term and the common ratio of a geometric sequence, the task is to find the sum of the infinite geometric series formed by the given first term and the common ratio.
Examples:
Input: A = 1, R = 0.5
Output: 2Input: A = 1, R = -0.25
Output: 0.8
Approach: The given problem can be solved based on the following observations:
- If absolute of value of R is greater than equal to 1, then the sum will be infinite.
- Otherwise, the sum of the Geometric series with infinite terms can be calculated using the formula
Therefore, if the absolute value of R is greater than equal to 1, then print “Infinite”. Otherwise, print the value 
as the resultant sum.
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <bits/stdc++.h>using namespace std;// Function to calculate the sum of// an infinite Geometric Progressionvoid findSumOfGP(double a, double r){ // Case for Infinite Sum if (abs(r) >= 1) { cout << "Infinite"; return; } // Store the sum of GP Series double sum = a / (1 - r); // Print the value of sum cout << sum;}// Driver Codeint main(){ double A = 1, R = 0.5; findSumOfGP(A, R); return 0;} |
Java
// Java program for the above approachimport java.util.*;class GFG{// Function to calculate the sum of// an infinite Geometric Progressionstatic void findSumOfGP(double a, double r){ // Case for Infinite Sum if (Math.abs(r) >= 1) { System.out.print("Infinite"); return; } // Store the sum of GP Series double sum = a / (1 - r); // Print the value of sum System.out.print(sum);}// Driver Codepublic static void main(String[] args){ double A = 1, R = 0.5; findSumOfGP(A, R);}}// This code is contributed by 29AjayKumar |
Python3
# Python3 program for the above approach# Function to calculate the sum of# an infinite Geometric Progressiondef findSumOfGP(a, r): # Case for Infinite Sum if (abs(r) >= 1): print("Infinite") return # Store the sum of GP Series sum = a / (1 - r) # Print the value of sum print(int(sum))# Driver Codeif __name__ == '__main__': A, R = 1, 0.5 findSumOfGP(A, R)# This code is contributed by mohit kumar 29. |
C#
// C# program for the above approachusing System;class GFG{ // Function to calculate the sum of // an infinite Geometric Progression static void findSumOfGP(double a, double r) { // Case for Infinite Sum if (Math.Abs(r) >= 1) { Console.Write("Infinite"); return; } // Store the sum of GP Series double sum = a / (1 - r); // Print the value of sum Console.Write(sum); } // Driver Code public static void Main() { double A = 1, R = 0.5; findSumOfGP(A, R); }}// This code is contributed by ukasp. |
Javascript
<script>// JavaScript program for the above approach// Function to calculate the sum of// an infinite Geometric Progressionfunction findSumOfGP(a, r){ // Case for Infinite Sum if (Math.abs(r) >= 1) { document.write("Infinite"); return; } // Store the sum of GP Series let sum = a / (1 - r); // Print the value of sum document.write(sum);}// Driver Codelet A = 1, R = 0.5;findSumOfGP(A, R);// This code is contributed by sanjoy_62 </script> |
Output:
2
Time Complexity: O(1)
Auxiliary Space: O(1), since no extra space has been taken.
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