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.

By Using for Loop
By Using while Loop
By Using User Defined Method

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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