Question

Prove by mathematical induction one of the following statements :

a) 1 · 2 + 2 · 3 + 3 · 4 + . . . + n(n + 1) = n(n+1)(n+2) 3 for all integer n ≥ 1.

b) u1 − u2 + u3 − u4 + . . . + (−1)n+1un = 1 + (−1)n+1un−1 for all integer n ≥ 1. (un denotes the nth Fibonacci number)

Answer 1

Here we are asked to prove one of the given statements. So we will prove the first one.