Question

What is the induction hypothesis assumption for the inequality m ! > 2^m where m>=4?

(a) for m=k, k+1!>2^k holds

(b) for m=k, k!>2^k holds

(c) for m=k, k!>3^k holds

(d) for m=k, k!>2^k+1 holds

The question was asked by my college professor while I was bunking the class.

My question is based upon Principle of Mathematical Induction topic in portion Induction and Recursion of Discrete Mathematics

Answer 1

Correct answer is (b) for m=k, k!>2^k holds

For explanation I would say: By the induction hypothesis, assume that p (k) = k! > 2^k is true, for m=k and we need to prove this by the principle of mathematical induction.