1. Prove by induction: when n is a natural number greater than 2, then 2^n> 2n+1.

5. Suppose that we have two algorithms for solving a particular type of problem. (A) Algorithm A solves the problem in 2^n seconds where n is an integer and is the size of the problem. (B) Algorithm B solves the problem in n^2+ 1,000,000 seconds. Show by induction that algorithm B is faster than algorithm A for all problem sizes greater than 19.