# Program to Find the Sum of Series 1+x+x^2+……+x^n

Posted in  Vinay Khatri
Last updated on September 28, 2023

## Problem Statement

We need to write a program that prints the sum of a special series ``` 1+x+x^2+……+x^n ``` . Here ``` x ``` is a variable and ``` n ``` represents the power up to which the series will go. For instance, consider that a user inputs x = 5 and n=6.

Input

``````x=5
n=6``````

Output

``19531``

The x and n values entered as 5 and 6, respectively, will follow this pattern: 1 + 5+ 5 2 + 5 3 +  5 4 + 5 5 + 5 6 = 19531

## Solution

Here are the steps that you need to follow to create a solution for the problem stated above:

• Initialize a variable ``` sum ``` with an initial value of 1.
• Ask the user to enter the values of x and n.
• Create a loop from range 1 to n.
• Inside the loop, add the value of x to the power n to the variable sum.

## C Program to Find the Sum of Series 1+x+x^2+……+x^n

``````#include <stdio.h>
#include <math.h>

int main()
{
int sum =1, x, n, i;
printf("Here we will calculate the sum of series 1+ x + x^2+ ...+ x^n \n");
printf("Enter the value of x: ");
scanf("%d", &x);

printf("Enter the value of n: ");
scanf("%d", &n);

for(i=1; i<=n;i++)
{
sum+=pow(x,i);
}

printf("The sum of the series is: %d", sum);

return 0;
}``````

Output:

``````Here we will calculate the sum of series 1+ x + x^2+ ...+ x^n
Enter the value of x: 5
Enter the value of n: 7
The sum of the series is: 97656``````

## C++ Program to Find the Sum of Series 1+x+x^2+……+x^n

``````#include<include>
#include<math.h>
using namespace std;
int main()
{
int sum=1,x,n,i;
cout<<"Here we will calculate the sum of series 1+ x + x^2+ ...+ x^n \n";

//input the value of x and n
cout<<"Enter the value of x: "; cin>>x;
cout<<"Enter the value of n: "; cin>>n;

for(i=1;i<=n;i++)
{
sum += pow(x,i);
}
cout<<"The sum of the series is: "<<sum;
return 0;
}``````

Output:

``````Here we will calculate the sum of series 1 +x +x^2 +……+ x^n

Enter the value of x: 5
Enter the value of n: 7
The sum of the series is: 97656``````

## Python Program to Find the Sum of Series 1+x+x^2+……+x^n

``````import math
sum=1
print("Here we will calculate the sum of series 1 +x +x^2 +……+ x^n")
x=int(input("Enter the value of x: "))
n = int(input("Enter the value of n: "))
for i in range(1,n+1):
sum+=math.pow(x,i)
print("The sum of the series is:", int(sum))``````

Output:

``````Here we will calculate the sum of series 1 +x +x^2 +……+ x^n

Enter the value of x: 3
Enter the value of n: 4
The sum of the series is: 121``````

## Java Program to Find the Sum of Series 1+x+x^2+……+x^n

``````import java.util.Scanner;
import java.lang.Math;
public class Main
{
public static void main(String[] args) {

int sum = 1, x, n, i;
Scanner sc = new Scanner (System.in);
System.out.println("We will calculate the sum of series 1+ x + x^2+ ...+ x^n \n");

//input the value of x and n
System.out.println("Enter the valyue of x:");
x = sc.nextInt();
System.out.println("Enter the valyue of n:");
n = sc.nextInt();

for(i=1;i<=n;i++)
{
sum += Math.pow(x,i);
}
System.out.println("The sum of the series is: " +sum);
}
}``````

Output

``````We will calculate the sum of series 1+ x + x^2+ ...+ x^n

Enter the valyue of x:
3
Enter the valyue of n:
4
The sum of the series is: 121``````

## Wrapping Up

In this programming tutorial, we discussed how to find the sum of series 1+x+x^2+……+x^n. We have written programs in C, C++, Python, and Java. To calculate the sum, we used the for loop . The time complexity of the above program is O(N), and the space complexity is constant.

If you have any queries, issues, or suggestions, please let us know by commenting them down below.