Question

Question 5
Write a menu driven program to find the sum of the following series depending on the
user choosing 1 or 2
1. S=1/4+1/8+1/12......... upto n terms
2. S=1/1!-2/2!+3/3!.......upto n terms
where ! stands for factorial of the number and the factorial value of a number is the
product of all integers from 1 to that number, e.g. 5! = 1 x 2 x 3 x 4 x 5.
(use switch-case).
[15​

Answer 1

refer above attachment

Answer 2

Series Sum - Java

We start by displaying the menu and taking the user input through Scanner class.

Then, we choose the corresponding block of code to execute with the switch-case structure.

Series 1

$\sf \displaystyle S = \frac{1}{4} + \frac{1}{8} + \frac{1}{12} + \dots + \frac{1}{4n}$

Clearly, the $\sf i^{th}$ term is $\sf\dfrac{1}{4 \times i}$ and we have to sum through it from i = 1 to i = n.

Series 2

$\sf\displaystyle S = \frac{1}{1!} - \frac{2}{2!} + \frac{3}{3!} - \dots + (-1)^{n+1} \frac{n}{n!}$

Here, the $\sf i^{th}$ term is $\sf (-1)^{i+1} \times \dfrac{i}{i!}$.

We also create a $\texttt{static int factorial(int n)}$ function to return the value of $\sf n!$.

It is a recursive function which works on the following basis:

$\sf n! = \begin{cases}\sf 1 & \sf if\ n=1 \\\sf n \times (n-1)! & \sf if\ n>1\end{cases}$

So, the factorial function looks like:

$\sf factorial(n) = \begin{cases}\sf 1 & \sf if\ n=1 \\\sf n \times factorial(n-1) & \sf if\ n>1\end{cases}$

If it feels too complex, just simply run a loop from 1 to n and return the product as follows:

static int factorial(int n) {

   int product = 1;

   for(int i = 1; i <= n; i++) {

       product = product * i;

   }

   return product;

}

Now, we come to the actual code.

$\rule{300}{1}$

SeriesSum.java

import java.util.Scanner;

public class SeriesSum {

   static int factorial(int n) {       //Factorial Function

       //This is a recursive function

       //Return n * (n-1) * (n-2) * ... * 1

       // n! = n * (n-1)!  

       //      with end condition as 1! = 1

       if(n == 1) {

           return 1;

       }

       else {

           return n*factorial(n-1);

       }

   }

   public static void main(String[] args) {

       Scanner sc = new Scanner(System.in);

       //Menu

       System.out.println("---Series Sum Menu---");

       System.out.println("1. S = 1/4 + 1/8 + 1/12... upto n terms");

       System.out.println("2. S = 1/1! - 2/2! + 3/3!... upto n terms");

       //Take user input of choice

       System.out.print("\nEnter 1 or 2: ");

       String choice = sc.next();

       int n;              //Number of terms

       double Sum = 0;     //Initialize Sum to 0

       switch(choice) {

           case "1":

               System.out.print("Enter value of n: ");

               n = sc.nextInt();

               

               for(double i = 1; i <= n; i++) {

                   Sum += 1 / (4*i);

               }

               System.out.println("Sum = "+Sum);

               break;

           case "2":

               System.out.print("Enter value of n: ");

               n = sc.nextInt();

               Sum = 0;

               

               for(int i = 1; i <= n; i++) {

                   Sum += Math.pow(-1, i+1) * (i / (double)factorial(i));

               }

               System.out.println("Sum = "+Sum);

               

               break;

           

           default:

               System.out.println("Invalid choice");

       }    

   }

}