Using java

Problem 1:

Create the following methods and test them using a TestRecursion class

A recursive method to draw rectangles like just like in the figure below.

A recursive method to calculate the factorial of a number

A recursive method to calculate the power of a number raised to another number ( power(x,n) is xn )

A recursive method to reverse a string.

A recursive method Vowels (st) that returns the number of vowels in a string st.

A recursive method to compute numbers in the Fibonacci sequence. This infinite sequence starts with 0 and 1, which we'll think of as the zeroth and first Fibonacci numbers, and each succeeding number is the sum of the two preceding Fibonacci numbers. Thus, the second number is 0 + 1 = 1. And to get the third Fibonacci number, we'd sum the first (1) and the second (1) to get 2. And the fourth is the sum of the second (1) and the third (2), which is 3. And so on.

n:0 1 2 3 4 5 6 7 8 9 10 11 ...

nthFibonacci:0 1 1 2 3 5 8 13 21 34 55 89 ...

A recursive method MaxR() to find the maximum of a numbers list ( Array, ArrayList and Linked List).

A recursive method SumR() to find the sum of a numbers list ( Array, ArrayList and Linked List).

A recursive method to convert from decimal to binary.

A recursive algorithm to multiply two positive integers m and n using repeated addition. Specify the

base case and the recursive case.

A recursive method to determine if a string is a Palindrome or not. (A Palindrome is a string that is the

same when read forwards or backwards after removing spaces).

Examples (Madam I m Adam) (Race car).

AmethodEX(x,n)tocalculatethevalueofex =1+(x/1!)+(x2 /2!)+(x3 /3!)+...+(xn /n!),Wheren

and x are supplied by the user. You must call 2 recursive methods (1 for factorial and another one for power (do not use pow method available in java).