JAVA

All recursive methods use conditional tests to either 1. stop or 2. continue the recursion. Each recursive method has the following characteristics: 1. end/terminating case: One or more end cases to stop the recursion. 2. recursive case: reduces the problem in to smaller sub-problems, until it reaches (becomes) the end case. Instructions: Complete the tasks listed below. Several pieces of starter code have been provided within this lab (my-api) to help you practice recursion. You are expected to implement the bodies of the recursive methods listed below and include them in your lab report by providing a summary of their implementation. Where to find starter code in 'my-work' repository package.class : modules.RecModule package.class : week03\$recursion.RecursionTest package.class : sierpinski.fill.Viewer Task Lists 1. Complete the body for the recursive method fac(n) which computes n ! ( n factorial) for n>=0. Note: n!=n(n1)(n2)(n2) (2) (1), where n>0 and zero factorial, 0!=1. 2. Complete the body for the recursive method sum(n) to compute the sum of the first n positive integers. 3. Complete the body for the recursive method pow (x,n) for computing xn, for a positive integer n, and real number x. 4. Complete the body for the recursive method isPalindrome(str) to determine if a string of text is a palindrome. This method accepts a String and returns true if the string reads the same forwards as backwards. The string is trivially true for empty or one(1) letter strings. Hint: You should make use of the substring and charAt methods of the String. 5. Run the Viewer of the Sierpinski Triangles and give a description of what you observed as it relates to recursion. Write a short summary ( 23 sentences is enough) of your observations. Feel free to explain what the recursive solution is doing by checking out its ControlPanel