Java Program to Find the Sum of Series x/2 + x/5 + x/8 + x/11 + …… + N

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

In this article we are going to see how to print the sum of series x/2 + x/5 + x/8 + … + N by using Java programming language.

Java Program to Find the Sum of Series x/2 + x/5 + x/8 + x/11 + …… + N

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

In Denominator, the number starts from 2 and the next number is the previous denominator number added with 3.

Example:

Suppose,
x = 2
n = 3

Then:
x/2 + x/5 + x/8  
= 2/2 + 2/5 + 2/8 
= 1+0.4 + 0.25 
= 1.65

Let’s see different ways to print the sum of series x/2 + x/5 + x/8 + … + N.

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

Method-1: Java Program to Find the Sum of Series x/2 + x/5 + x/8 + x/11 + …… + 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.
Create Scanner class object.
Prompt the user to enter values for x and n.
Use a for loop from i=2 to i<=n*n and incremented by 3.
Inside loop we will find the value of x/i and then we will add that value in sum in each iteration.
Then we will increment the count value, and then we will check if the count value is equal to n or not. If count is equal to n then we will break our loop.
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 nth term 'n' ");
        int n = s.nextInt();
        //for loop to print the series
        double sum = 0;
       int count = 0;
       for (int i = 2; i <= n*n; i = i+3)
       {
            sum += (double)x / i;
           count++;
           if(count == n)
           break;
       }        
        System.out.println("Sum of the series is " + sum);
    }
}

Output:

Enter the value of x 
2
Enter the nth term 'n' 
3
Sum of the series is 1.65

Method-2: Java Program to Find the Sum of Series x/2 + x/5 + x/8 + x/11 + …… + 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.
Create Scanner class object.
Prompt the user to enter values for x and n.
Initialize integer variable ‘i‘ with value 2.
Use a while loop from till i<=n*n and incremented by 3.
Inside loop we will find the value of x/i and then we will add that value in sum in each iteration.
Then we will increment the count value, and then we will check if the count value is equal to n or not. If count is equal to n then we will break our loop.
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 nth term 'n' ");
        int n = s.nextInt();
        //while loop to print the series
        double sum = 0;
        int i = 2;
        int count=0;
       while(i <= n*n) 
        {
            sum += (double)x / i;
           count ++;
           if(count == n)
            break;
            i +=3;
        }
        System.out.println("sum of the series is " + sum);
    }
}

Output:

Enter the value of x 
2
Enter the nth term 'n' 
3
sum of the series is 1.65

Method-3: Java Program to Find the Sum of Series x/2 + x/5 + x/8 + x/11 + …… + 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.
Create Scanner class object.
Prompt the user to enter values for x and n.
Call a user defined method say m1() and pass x and n as parameter.
Inside method use a for loop from i=2 to i<=n*n and incremented by 3.
Inside loop we will find the value of x/i and then we will add that value in sum in each iteration.
Then we will increment the count value, and then we will check if the count value is equal to n or not. If count is equal to n then we will break our loop.
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 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;
       int count = 0;
       for (int i = 2; i <= n*n; i = i+3)
       {
            sum += (double)x / i;
           count++;
           if(count == n)
            break;
       }
        System.out.println("Sum of the series is " + sum);
    }
}

Output:

Enter the value of x 
5
Enter the nth term 'n' 
7
Sum of the series is 5.480805958747134

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