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# Find the sum of the series x(x+y) + x^2(x^2+y^2) +x^3(x^3+y^3)+ … + x^n(x^n+y^n)

• Difficulty Level : Medium
• Last Updated : 30 Aug, 2022

Given a series where x, y and n take integral values. The task is to Find the sum till nth term of the given series.
Examples:

Input: x = 2, y = 2, n = 2
Output: 40

Input: x = 2, y = 4, n = 2
Output: 92

Approach: Given series is :

Thus our problem reduces to finding sum of two GP series.
Below is the implementation of above approach:

## C++

 // CPP program to find the sum of series #include  using namespace std;   // Function to return required sum int sum(int x, int y, int n) {       // sum of first series     int sum1 = (pow(x, 2) * (pow(x, 2 * n) - 1))                / (pow(x, 2) - 1);       // sum of second series     int sum2 = (x * y * (pow(x, n) * pow(y, n) - 1))                / (x * y - 1);       return sum1 + sum2; }   // Driver Code int main() {     int x = 2, y = 2, n = 2;       // function call to print sum     cout << sum(x, y, n);     return 0; }

## Java

 // Java program to find the sum of series    public class GFG {           // Function to return required sum      static int sum(int x, int y, int n)      {                // sum of first series          int sum1 = (int) (( Math.pow(x, 2) * (Math.pow(x, 2 * n) - 1))                     / (Math.pow(x, 2) - 1));                // sum of second series          int sum2 = (int) ((x * y * (Math.pow(x, n) * Math.pow(y, n) - 1))                     / (x * y - 1));                return sum1 + sum2;      }            // Driver code      public static void main (String args[]){         int x = 2, y = 2, n = 2;                    // function call to print sum          System.out.println(sum(x, y, n));      }   // This code is contributed by ANKITRAI1 }

## Python3

 # Python3 program to find the sum of series  # Function to return required sum    def sum(x,y,n):           # sum of first series      sum1 = ((x**2)*(x**(2*n)-1))//(x**2 - 1)           # sum of second series     sum2 = (x*y*(x**n*y**n-1))//(x*y-1)     return (sum1+sum2)       # Driver Code  if __name__=='__main__':     x = 2     y = 2     n = 2 # function call to print sum      print(sum(x, y, n))       # this code is contributed by sahilshelangia

## C#

 // C# program to find the sum of series  using System;   class GFG  {   // Function to return required sum  static int sum(int x, int y, int n)  {        // sum of first series      int sum1 = (int) ((Math.Pow(x, 2) *                        (Math.Pow(x, 2 * n) - 1)) /                       (Math.Pow(x, 2) - 1));        // sum of second series      int sum2 = (int) ((x * y * (Math.Pow(x, n) *                 Math.Pow(y, n) - 1)) / (x * y - 1));        return sum1 + sum2;  }    // Driver code  public static void Main () {     int x = 2, y = 2, n = 2;            // function call to print sum      Console.Write(sum(x, y, n));  } }   // This code is contributed by ChitraNayal

## PHP

 

## Javascript

 

Output:

40

Time Complexity: O(log(n))

Auxiliary Space: O(1)

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