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

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

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In the previous article, we have discussed about Java Program to Print Series 3 6 9 12 15 18 …N

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

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

Let’s see different ways to find the series.

Method-1: Java Program to Print the Sum of Series (1+2)/(1*2) + (1+2+3)/(1*2*3) + …… + (1+2+3+…+N)/(1*2*3*…*N) By Using User Input Value

Approach:

  • Create Scanner class object.
  • Prompt the user to enter a number.
  • Initialize the variable sum = 0.
  • Run a for loop i=2 to n+1(otherwise it won’t print the desired sum).
  • Inside the loop, initialize two variables num and den both to 0.
  • Run a nested for loop j=1 to i and update num+=j and den as den*=j.
  • Then outside the inner loop update sum variable as sum = sum + num/den.
  • Print the result outside the loops.

Program:

import java.util.Scanner;
public class Main
{
    public static void main(String args[]) 
    {
        // create scanner class object
        Scanner in = new Scanner(System.in);
        // take user input
        System.out.print("Enter n: ");
        int n = in.nextInt();
        // initialize sum to 0
        double sum = 0.0;
        // loop to find the sum of the series
        for (int i = 2; i <= (n+1); i++)
        {
            double num = 0.0, den = 1.0;
            // inner loop to calculate numerator
            // and denominator at ith positon
            for (int j = 1; j <= i; j++) 
            {
                num += j;
                den *= j;
            }
            // updating sum variable
            sum = sum + (num / den);
        }
        // printing the result
        System.out.println("Sum=" + sum);
    }
}

Output:

Enter n: 5
Sum=3.0708333333333333

Method-2: Java Program to Print the Sum of Series (1+2)/(1*2) +  (1+2+3)/(1*2*3) + …… + (1+2+3+…+N)/(1*2*3*…*N) By Using User-Defined Method

  • In method 1, a lot of things were happening inside the for loop and it’s hard to figure out what actually is the program doing.
  • Therefore, it is usually preferable to break down the programs into subtasks and define methods as required.
  • In this case the program primarily has 3 subtasks
    1. Finding sum upto ith position
    2. Finding product upto ith position
    3. Dividing sum by product.
    4. And finally, the addition of the terms.
  • The 3rd and the 4th subtasks are just one liners and hinder the readability of the code but task 1 and 2 are a bit lengthy and relatively complicated so we may move them into new methods and call these methods in the driver method (in this case the main method)

Approach:

  • Create Scanner class object.
  • Prompt the user to enter a number.
  • Initialize the variable sums = 0.
  • Run a for loop i=2 to n+1.
  • Inside the loop, update sums = sums + sum(i) / product(i);
  • Here the sum() and product are user defined methods which will return the sum and product (num and den in method 1 respectively).
  • Print sums outside the loop.
  • Now define a method product which takes an argument i of integer type and returns a double.
  • Inside the method initialize a variable prod as 1.0
  • Run a for loop j=1 to i and update prod as prod *= j.
  • Similarly, define a method sum which takes an argument i of integer type and returns a double.
  • Inside the method initialize a variable s as 0.0
  • Run a for loop j=1 to i and update s as s += j

Program:

import java.util.Scanner;
public class Main 
{
    public static void main(String[] args) 
    {
        // create a Scanner object
        Scanner sc = new Scanner(System.in);
        // prompt the user to enter the number of terms
        System.out.print("Enter the number of terms: ");
        int n = sc.nextInt();
        // initialize sum variable
        double sums = 0.0;
        // call the method to print the series
        for (int i = 2; i <= (n + 1); i++)
        {
            sums += sum(i) / product(i);
        }
        System.out.println("The sum of the series is: " + sums);
    }

    // method to find the product from 1 to i
    private static double product(int i) 
    {
        double prod = 1;
        for (int j = 1; j <= i; j++) 
        {
            prod *= j;
        }
        return prod;
    }

    // method to find the sum from 1 to i
    private static double sum(int i) {
        double s = 0.0;
        for (int j = 1; j <= i; j++) {
            s += j;
        }
        return s;
    }

}

Output:

Enter the number of terms: 5
The sum of the series is: 3.0708333333333333

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