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# Find the sum of infinite series 1^2.x^0 + 2^2.x^1 + 3^2.x^2 + 4^2.x^3 +…….

• Difficulty Level : Hard
• Last Updated : 31 Aug, 2022

Given an infinite series and a value x, the task is to find its sum. Below is the infinite series

1^2*x^0 + 2^2*x^1 + 3^2*x^2 + 4^2*x^3 +……. upto infinity, where x belongs to (-1, 1)

Examples:

Input: x = 0.5
Output: 12

Input: x = 0.9
Output: 1900

Approach:
Though the given series is not an Arithmetico-Geometric series, however, the differences and so on, forms an AP. So, we can use the Method of Differences. Hence, the sum will be (1+x)/(1-x)^3.
Below is the implementation of above approach:

## C++

 // C++ implementation of above approach #include  #include    using namespace std;   // Function to calculate sum double solve_sum(double x) {     // Return sum     return (1 + x) / pow(1 - x, 3); }   // Driver code int main() {     // declaration of value of x     double x = 0.5;       // Function call to calculate     // the sum when x=0.5     cout << solve_sum(x);       return 0; }

## Java

 // Java Program to find  //sum of the given infinite series import java.util.*;   class solution { static double calculateSum(double x) {       // Returning the final sum return (1 + x) / Math.pow(1 - x, 3);   }   //Driver code public static void main(String ar[]) {         double x=0.5;   System.out.println((int)calculateSum(x));   } } //This code is contributed by Surendra_Gangwar

## Python

 # Python implementation of above approach   # Function to calculate sum def solve_sum(x):     # Return sum     return (1 + x)/pow(1-x, 3)   # driver code   # declaration of value of x x = 0.5   # Function call to calculate the sum when x = 0.5 print(int(solve_sum(x)))

## C#

 // C# Program to find sum of // the given infinite series using System;   class GFG { static double calculateSum(double x) {       // Returning the final sum return (1 + x) / Math.Pow(1 - x, 3);   }   // Driver code public static void Main() {     double x = 0.5;     Console.WriteLine((int)calculateSum(x)); } }   // This code is contributed // by inder_verma..

## PHP

 

## Javascript

 

Output:

12

Time Complexity: O(1)

Auxiliary Space: O(1)

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