To solve a problem using recursion, it is broken down into sub-problems . Each sub- aroblom is the same as the oniginal probilem, but smaller in size. You can apply the same approach to each sub-problem to solve it recursively. ALL recursive methods have the following characteristics The method is implemented using a test to stop or continue the recursion, such as ir- elne statements that leads to different cases end case: One or more end cases (the simplest case) that are used to terminate 2 ecursive case: A recursive call that reduces the original problem, bringing in oreasingly closer to the end case until it becomes that case Recursive Algorithms 1. Many mathematical functions are defined with recursion. For instance, the factorial of a positive number n. n! nin - 1) (n - 2) (n-2) (2) (1), wheren>o Write a recursive algorithm to compute n 2. The Fibonacci series is a mathematical model that is often used in tonether. T optimization. It is based on a sequence of numbers series begins with O and 1, and each preceding two. that are added together. The subsequent number is the sum of the Example value: o Write a recursive algorithm to compute the Fibon 5. Write a recursive algorithm for computing 2" fora into a Java code method implementation, Write out the result for your methood implementation when n 5. Show ALL steps in the process. 6. Write a recursive algorithm for computing " for a positive integer n, and real Java code method implementation. Write out the number result for your method implementation when n = 5 and x = e. Show ALL steps in the x, then translate into 3. Write a recursive method to compute the sum of the first n positive integers. Test if your solution is correct in Java. 4. Write a recursive method to compute the sum of the first n positive odd integers. Test if your solution is correct in Java