n Java trace the table for a while loop  public class Main { public static void main(String[] args) { // Question 2 j = 30; x=5; for (int i=1;i<=2;i++) { while (j > 20) { j=j-x*i; ++x; }// end of while }// end of for j x i j<=2 j>20

Part (1) Write a recursion method named CalculateSeries, that will receive one integer valuen as parameter. The method will calculate and return the term n in the following series: T(0)= 0 T(n)= 2 T(n-1) +1 Part (2) Write the main method to test your method. Enter n >> 5 T(5) = 31 %3D

Code 16-1   /** This class has a recursive method.  */    public class EndlessRecursion {    public static void message() {    System.out.println("This is a recursive method.");  message();  } }   Code 16.2   /**  This class has a recursive method message,  which displays a message n times.  */   public class Recursive {  public static void messge (int n) {    if (n>0) {    System.out.println (" This is a recursive method.");  message(n-1);  } } }     Task #1 Tracing Recursive Methods 1. Copy the file Recursion.java (see Code Listing 16.1) from the Student Files or as directed by your instructor. 2. Run the program to confirm that the generated answer is correct. Modify the factorial method in the following ways: a. Add these lines above the first if statement: int temp; System.out.println("Method call -- " + "calculating " + "Factorial of: " + n); Copyright © 2019 Pearson Education, Inc., Hoboken NJ b. Remove this line in the recursive section at the end of the method: return…

1. Write a recursive method expFive(n) to compute y=5^n. For instance, if n is 0, y is 1. If n is 3, then y is 125. If n is 4, then y is 625. The recursive method cannot have loops. Then write a testing program to call the recursive method. If you run your program, the results should look like this: > run RecExpTest Enter a number: 3 125 >run RecExpTest Enter a number: 3125 2. For two integers m and n, their GCD(Greatest Common Divisor) can be computed by a recursive function. Write a recursive method gcd(m,n) to find their Greatest Common Divisor. Once m is 0, the function returns n. Once n is 0, the function returns m. If neither is 0, the function can recursively calculate the Greatest Common Divisor with two smaller parameters: One is n, the second one is m mod n. Although there are other approaches to calculate Greatest Common Divisor, please follow the instructions in this question, otherwise you will not get the credit. Meaning your code needs to follow the given algorithm. Then…