1. Use induction to prove that for all integers n 2:

(1-1/2)*(1-1/3)*(1-1/4)*.....*(1-1/n) = 1/n

2. Use induction to prove that for all integers n 1:

2 2^1 +3 2^2 +4 2^3 +...+(n+1) 2^n = n 2^(n+1).