Use the following three mathematical functions (assume N >= 0):

- Sum(N) = 1 + 2 + 3 + ... + N

- BiPower(N) = 2^N

- TimesFive(N) = 5N

1. Define recursively using your math knowledge.

a. Sum(N)

b. BiPower(N)

c. TimesFive(N)

2. Create a recursive program that prompts the user for a non-negative integer N and outputs. Describe any input constraints in the opening comment of your recursive methods.

a. Sum(N)

b. BiPower(N)

c. TimesFive(N)

d. Fib(N)

The Fibonacci sequence is the series of integers 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 ... See the pattern? Each element in the series is the sum of the preceding two elements. Here is a recursive definition the Fibonacci sequence:

Fib(N) =

N if N = 0 or 1

Fib(N - 2) + Fib(N - 1) if N > 1

[ Extra Credit]

Write a nonrecursive version of the method Fib.