Java Program to Find the Sum of Series (1/2) + (2/3) + (3/4) + …… + N

In the previous article we have discussed about Java Program to Find the Sum of Series 1 + (1/3) + (1/5) + … + N

In this article we are going to see how to print sum of the series (1/2) + (2/3) + (3/4) + …… + N by using Java programming language.

Java Program to Find the Sum of Series (1/2) + (2/3) + (3/4) + …… + N

On observing the pattern carefully, we can see each term is in a/b format.

Numerator = Starts from 1 and in each term incremented by 1

Denominator = In each term Numerator+1

1st term=1/2

2nd term=2/3

3rd term=3/4 like this.

And the series= 1/2+2/3+3/4 like this.

And our task is to first form the series and then find the sum of the series.

Let’s see different ways to print sum of the series (1/2) + (2/3) + (3/4) + …… + N.

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

Example:

Suppose value of n = 3

(1/2) + (2/3) + (3/4) 
= 0.5+0.66+0.75 
= 1.91

Method-1: Java Program to Find the Sum of Series (1/2) + (2/3) + (3/4) + …… + N By Using For Loop

Approach:

Declare an integer variable say ‘n’ which holds the value of Nth term.
Create Scanner class object.
Prompt the user to enter a number as value of n.
Declare an long variable say ‘sum‘ and initialize it to 0.
Use a for loop from i=1 to i<=100 (incremented by 1)
Inside the for loop, find each term and add it to sum.
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 'n' ");
        int n = s.nextInt();
        double sum = 0;
        //for loop to print the series
        for (int i = 1; i <= n; i++)
        {   
            sum += ( i/(double)(i+1));
        }
        System.out.println("Sum of the series is " + sum);
    }
}

Output:

Enter the value of 'n' 
3
Sum of the series is 1.9166666666666665

Method-2: Java Program to Find the Sum of Series (1/2) + (2/3) + (3/4) + …… + N By Using While Loop

Approach:

Declare an integer variable say ‘n’ which holds the value of Nth term.
Create Scanner class object.
Prompt the user to enter a number as value of n.
Declare an long variable say ‘sum‘ and initialize it to 0.
Use a for loop from i=1 to i<=100 (incremented by 1)
Inside the for loop, find each term and add it to sum.
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 'n' ");
        int n = s.nextInt();
        double sum = 0;
        int i=1;
        //while loop to print the series
        while (i <= n)
        {   
            sum += ( i/(double)(i+1));
            i++;
        }
        System.out.println("Sum of the series is " + sum);
    }
}

Output:

Output: Enter the value of 'n' 
3
Sum of the series is 1.9166666666666665

Method-3: Java Program to Find the Sum of Series (1/2) + (2/3) + (3/4) + …… + N By Using While Loop

Approach:

Declare an integer variable say ‘n’ which holds the value of Nth term.
Create Scanner class object.
Prompt the user to enter a number as value of n.
Then call a user defined method say printSeries() by passing n as parameter.
Inside method declare an long variable say ‘sum‘ and initialize it to 0.
Use a for loop from i=1 to i<=100 (incremented by 1)
Inside the for loop, find each term and add it to sum.
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 'n' ");
        int n = s.nextInt();
        //calling printSeries() method to print the series
        printSeries(n);
   }
    public static void printSeries(int n)
    {
        double sum = 0;
        //for loop to print the series
        for (int i = 1; i <= n; i++)
        {
            sum += ( i/(double)(i+1));
        }
        System.out.println("Sum of the series is " + sum);
    }
}

Output:

Enter the value of 'n' 
5
Sum of the series is 3.5500000000000003

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