# Java Program to Find the Sum of Series 1/x + 1/x^2 + 1/x^3 + …… + 1/x^n

In the previous article, we have discussed about Java Program to Find the Sum of Series 1^2/a + 3^2/a^2 + 5^2/a^3 + …… + N

In this article we are going to see how to find sum of the series 1/x + 1/x^2 + 1/x^3 + …… + 1/x^n by using Java programming language.

## Java Program to Find the Sum of Series 1/x + 1/x^2 + 1/x^3 + …… + 1/x^n

On observing the pattern carefully, we can see Numerator is 1 (fixed)

In Denominator, the power/exponent of x is increasing by 1

Example:

x = 2
n = 3

1/2 + 1/2^2 + 1/2^3
= 1/2 + 1/4 + 1/8
= 0.5 + 0.25 + 0.125
= 0.875

Let’s see different ways to find sum of the series 1/x + 1/x^2 + 1/x^3 + …… + 1/x^n.

### Method-1: Java Program to Find the Sum of Series 1/x + 1/x^2 + 1/x^3 + …… + 1/x^n By Using For Loop

Approach:

• Declare an integer variable say ‘x’ which holds the value of “x”.
• Declare an integer variable say ‘n’ which holds the nth term of the series “n”.
• Create Scanner class object.
• Prompt the user to enter value of x and n.
• Use a for loop from i=1 to i<=n
• Inside loop we will first find the value of 1/Math.pow(x,i) and then we will add the value in sum in every iteration.
• Print the result.

Program:

import java.util.*;
public class Main
{
public static void main(String args[])
{
//creating object of Scanner class
Scanner s = new Scanner(System.in);
//Taking input of number of elements in the series
System.out.println("Enter the value of x ");
int x = s.nextInt();
//Taking input of number of elements in the series
System.out.println("Enter the value of nth term 'n' ");
int n = s.nextInt();
//for loop to print the series
double sum = 0;
for (int i = 1; i <= n; i++)
sum += 1 / Math.pow(x, i);
System.out.println("Sum of the series is " + sum);
}
}

Output:

Enter the value of x
2
Enter the value of nth term 'n'
3
Sum of the series is 0.875

### Method-2: Java Program to Find the Sum of Series 1/x + 1/x^2 + 1/x^3 + …… + 1/x^n By Using While Loop

Approach:

• Declare an integer variable say ‘x’ which holds the value of “x”.
• Declare an integer variable say ‘n’ which holds the nth term of the series “n”.
• Create Scanner class object.
• Prompt the user to enter value of x and n.
• Use a while loop from i=1 to i<=n
• Inside loop we will first find the value of 1/Math.pow(x,i) and then we will add the value in sum in every iteration.
• Print the result.

Program:

import java.util.*;
public class Main
{
public static void main(String args[])
{
//creating object of Scanner class
Scanner s = new Scanner(System.in);
//Taking input of number of elements in the series
System.out.println("Enter the value of x ");
int x = s.nextInt();
//Taking input of number of elements in the series
System.out.println("Enter the value of nth term 'n' ");
int n = s.nextInt();
//while loop to print the series
double sum = 0;
int i = 1;
while(i <= n)
{
sum += 1 / Math.pow(x, i);
i ++;
}
System.out.println("sum of the series is " + sum);
}
}

Output:

Enter the value of x
2
Enter the value of nth term 'n'
3
sum of the series is 0.875

### Method-3: Java Program to Find the Sum of Series 1/x + 1/x^2 + 1/x^3 + …… + 1/x^n By Using User Defined Method

Approach:

• Declare an integer variable say ‘x’ which holds the value of “x”.
• Declare an integer variable say ‘n’ which holds the nth term of the series “n”.
• Create Scanner class object.
• Prompt the user to enter value of x and n.
• Call a method m1() by passing x and n as parameter.
• Inside method use a for loop from i=1 to i<=n
• Inside loop we will first find the value of 1/Math.pow(x,i) and then we will add the value in sum in every iteration.
• Print the result.

Program:

import java.util.*;
public class Main
{
public static void main(String[] args)
{
// creating object of scanner class
Scanner s = new Scanner(System.in);
//Taking input of number of elements in the series
System.out.println("Enter the value of x ");
int x = s.nextInt();
//Taking input of number of elements in the series
System.out.println("Enter the value of nth term 'n' ");
int n = s.nextInt();
// calling m1 method to print the series
m1(x,n);
}
public static void m1(int x, int n)
{
//for loop to print the series
double sum = 0;
for (int i = 1; i <= n; i++)
sum += 1 / Math.pow(x, i);
System.out.println("Sum of the series is " + sum);
}
}

Output:

Enter the value of x
5
Enter the value of nth term 'n'
10
Sum of the series is 0.24999997440000005

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