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.
People are also reading:
 WAP to calculate sum and average of three numbers
 WAP to calculate area of a circle, a rectangle or a triangle
 Python Program to Find Numbers Divisible by Another Number
 Python Program to Display the Multiplication Table
 WAP in C++ and Python to calculate 3X3 Matrix multiplication
 Python Program to Illustrate Different Set Operations
 Python Program to Find Factorial of Number Using Recursion
 WAP in C++ & Python for Armstrong Number
 Python Program to Convert Kilometers to Miles
 Python Program to Solve Quadratic Equation
Leave a Comment on this Post