5. We denote fn as the n-th Fibonacci number. (a) Prove the following statement by induction: For n 1, 12 +3 4 + ... + (1)n-n = (1)n-1 + (1)n-n = (1)n-1 n(n + 1) 2 - n-1 (b) Prove by induction that for each integer n 2, fn < (7)1. (c) Prove that gcd(fn, fn+1) = 1 for every n 1. (d) Show by induction on n that for n 0, n fi = fn+2 -1. i=0 (e) Prove (fn)2 = fn1n+1 (1)n, for n Z+.