Originally Posted by

**yoman360** So I have an exam tomorrow for my discrete math class and I was doing the suggested practice problems for the exam. So far I understand and know how to do all the types of induction problems except the inequality proofs.

I know how to start off the inequality proof, but I don't how to finish it.

Prove $\displaystyle 2n+1 < 2^n$ for all integers n >= 3

__Proof__: Let P(n) be the predicate: $\displaystyle 2n+1 < 2^n$

__Basis Step__: P(3) says:

2(3) + 1 < 2^3

7 < 8 <== this is true!

__Inductive Step__: Assume P(n) is true, prove P(n+1)

P(n+1) ==> 2(n+1)+1 < 2^(n+1)