Use mathematical induction to prove that for all natural numbers $4^n < 5^n$?

Question

I'm stuck at the inductive step, which is $4^{k+1} < 5^{k+1}$ , where $k> 0$. Any help would be much appreciated on how to prove my inductive hypothesis.

Does this answer your question? Induction Proof $4^k < 5^k$ – Martin R Mar 11 '21 at 05:05 — Martin R, Mar 11 '21 at 05:05
Another one: https://math.stackexchange.com/q/4056737/42969 – Martin R Mar 11 '21 at 05:07 — Martin R, Mar 11 '21 at 05:07

P. J. · Accepted Answer · 2021-03-11T05:04:56.877

-1

$$ 4^{k+1} = 4\cdot4^k < 4\cdot 5^k < 5\cdot5^k =5^{k+1}$$

edited Mar 11 '21 at 05:04

answered Mar 11 '21 at 04:56

P. J.

646

Thanks! It understood it now. – user11233 Mar 11 '21 at 09:24

Use mathematical induction to prove that for all natural numbers $4^n < 5^n$?

1 Answers1