I tried to prove but I confused. Can you help me, please?

Question

Prove by induction:

$2^n\ge n^2$ for all $n\ge 5$.

Answer 1

Well your first step should be to prove it when n = 5. This will be your base case scenario. From there you need to prove it for n = k + 1. Simply plug in k + 1 for n in your equation (2^n >= n^2). Your new equation will be (2^(k+1) >= (k+1)^2). Simply step through the algebra at this point.