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 <iostream>#include <math.h>using namespace std;// Function to calculate sumdouble solve_sum(double x){ // Return sum return (1 + x) / pow(1 - x, 3);}// Driver codeint 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 seriesimport java.util.*;class solution{static double calculateSum(double x){ // Returning the final sumreturn (1 + x) / Math.pow(1 - x, 3);}//Driver codepublic 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 sumdef solve_sum(x): # Return sum return (1 + x)/pow(1-x, 3)# driver code# declaration of value of xx = 0.5# Function call to calculate the sum when x = 0.5print(int(solve_sum(x))) |
C#
// C# Program to find sum of// the given infinite seriesusing System;class GFG{static double calculateSum(double x){ // Returning the final sumreturn (1 + x) / Math.Pow(1 - x, 3);}// Driver codepublic static void Main(){ double x = 0.5; Console.WriteLine((int)calculateSum(x));}}// This code is contributed// by inder_verma.. |
PHP
<?php// PHP implementation of // above approach// Function to calculate sumfunction 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=0.5echo solve_sum($x);// This code is contributed// by inder_verma?> |
Javascript
<script>// javascript Program to find //sum of the given infinite seriesfunction calculateSum(x){ // Returning the final sumreturn (1 + x) / Math.pow(1 - x, 3);}//Driver code var x=0.5;document.write(parseInt(calculateSum(x)));// This code is contributed by 29AjayKumar </script> |
Output:
12
Time Complexity: O(1)
Auxiliary Space: O(1)
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