# Program to find the sum of the series 1 + x + x^2+ x^3+ .. + x^n

• Difficulty Level : Medium
• Last Updated : 12 Jul, 2022

Given an integer X, the task is to print the series and find the sum of the series
Examples :

Input: X = 2, N = 5
Output: Sum = 31
1 2 4 8 16
Input: X = 1, N = 10
Output: Sum = 10
1 1 1 1 1 1 1 1 1 1

Approach: The idea is to traverse over the series and compute the sum of the N terms of the series. The Nth term of the series can be computed as:

Nth Term = (N-1)th Term * X

Below is the implementation of the above approach:

## C++

 `// C++ implementation to find` `// sum of series of` `// 1 + x^2 + x^3 + ....+ x^n`   `#include `   `using` `namespace` `std;`   `// Function to find the sum of` `// the series and print N terms` `// of the given series` `double` `sum(``int` `x, ``int` `n)` `{` `    ``double` `i, total = 1.0, multi = x;`   `    ``// First Term` `    ``cout << total << ``" "``;`   `    ``// Loop to print the N terms` `    ``// of the series and find their sum` `    ``for` `(i = 1; i < n; i++) {`   `        ``total = total + multi;` `        ``cout << multi << ``" "``;` `        ``multi = multi * x;` `    ``}`   `    ``cout << ``"\n"``;` `    ``return` `total;` `}`   `// Driver code` `int` `main()` `{` `    ``int` `x = 2;` `    ``int` `n = 5;` `    ``cout << fixed` `         ``<< setprecision(2)` `         ``<< sum(x, n);` `    ``return` `0;` `}`

## C

 `// C implementation to find the sum` `// of series 1 + x^2 + x^3 + ....+ x^n`   `#include ` `#include `   `// Function to print the sum` `// of the series` `double` `sum(``int` `x, ``int` `n)` `{` `    ``double` `i, total = 1.0, multi = x;`   `    ``// First Term of series` `    ``printf``(``"1 "``);`   `    ``// Loop to find the N` `    ``// terms of the series` `    ``for` `(i = 1; i < n; i++) {`   `        ``total = total + multi;` `        ``printf``(``"%.1f "``, multi);` `        ``multi = multi * x;` `    ``}` `    ``printf``(``"\n"``);` `    ``return` `total;` `}`   `// Driver Code` `int` `main()` `{` `    ``int` `x = 2;` `    ``int` `n = 5;` `    ``printf``(``"%.2f"``, sum(x, n));` `    ``return` `0;` `}`

## Java

 `// Java implementation to find` `// the sum of series` `// 1 + x^2 + x^3 + ....+ x^n`   `class` `GFG {`   `    ``// Java code to print the sum` `    ``// of the given series` `    ``static` `double` `sum(``int` `x, ``int` `n)` `    ``{` `        ``double` `i, total = ``1.0``, multi = x;`   `        ``// First Term` `        ``System.out.print(``"1 "``);`   `        ``// Loop to print the N terms` `        ``// of the series and compute` `        ``// their sum` `        ``for` `(i = ``1``; i < n; i++) {` `            ``total = total + multi;` `            ``System.out.print(multi);` `            ``System.out.print(``" "``);` `            ``multi = multi * x;` `        ``}`   `        ``System.out.println();` `        ``return` `total;` `    ``}`   `    ``// Driver Code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `x = ``2``;` `        ``int` `n = ``5``;` `        ``System.out.printf(` `            ``"%.2f"``, sum(x, n));` `    ``}` `}`

## Python3

 `# Python3 program to find sum of ` `# series of 1 + x^2 + x^3 + ....+ x^n `   `# Function to find the sum of ` `# the series and print N terms ` `# of the given series ` `def` `sum``(x, n): ` `    `  `    ``total ``=` `1.0` `    ``multi ``=` `x `   `    ``# First Term ` `    ``print``(``1``, end ``=` `" "``) `   `    ``# Loop to print the N terms ` `    ``# of the series and find their sum ` `    ``for` `i ``in` `range``(``1``, n): ` `        `  `        ``total ``=` `total ``+` `multi ` `        ``print``(``'%.1f'` `%` `multi, end ``=` `" "``) ` `        ``multi ``=` `multi ``*` `x ` `        `  `    ``print``(``'\n'``)` `    ``return` `total; `   `# Driver code ` `x ``=` `2` `n ``=` `5` `print``(``'%.2f'` `%` `sum``(x, n))`   `# This code is contributed by Pratik Basu `

## C#

 `// C# implementation to find` `// the sum of series` `// 1 + x^2 + x^3 + ....+ x^n` `using` `System;` `class` `GFG{`   `// C# code to print the sum` `// of the given series` `static` `double` `sum(``int` `x, ``int` `n)` `{` `    ``double` `i, total = 1.0, multi = x;`   `    ``// First Term` `    ``Console.Write(``"1 "``);`   `    ``// Loop to print the N terms` `    ``// of the series and compute` `    ``// their sum` `    ``for` `(i = 1; i < n; i++)` `    ``{` `        ``total = total + multi;` `        ``Console.Write(multi);` `        ``Console.Write(``" "``);` `        ``multi = multi * x;` `    ``}` `    ``Console.WriteLine();` `    ``return` `total;` `}`   `// Driver Code` `public` `static` `void` `Main(String[] args)` `{` `    ``int` `x = 2;` `    ``int` `n = 5;` `    ``Console.Write(``"{0:F2}"``, sum(x, n));` `}` `}`   `// This code is contributed by Rajput-Ji`

## Javascript

 ``

Output:

```1 2.0 4.0 8.0 16.0
31.00```

Time Complexity: O(n)

Auxiliary Space: O(1), since no extra space has been taken.

My Personal Notes arrow_drop_up
Related Articles