2 Fibonacci sequence 1. Find a closed form for the terms of the Fibonacci sequence by solving the homogeneous constant coefficient recursion fo = 0, f1 = 1 and fn = fn-1+fn-2. 2. Prove that Sn = fo + f1+ ... + fn is equal to fn+2 - 1. 3. Prove that fn is even if and only if n is divisible by 3. 4. Find a rational function whose Maclaurin series is equal to the gener- ating function of the Fibonacci sequence