For which integers is 3^n > n^3?

it seems to be for all but 3, but I am stuck on the proof.

Assume 3^n > n^3

n>3

Then

3^(n+1) > 3*n^3

Now what?

Printable View

- Aug 2nd 2011, 02:57 PMveronicak5678Inductive Proof
For which integers is 3^n > n^3?

it seems to be for all but 3, but I am stuck on the proof.

Assume 3^n > n^3

n>3

Then

3^(n+1) > 3*n^3

Now what? - Aug 2nd 2011, 04:14 PMPlatoRe: Inductive Proof
- Aug 2nd 2011, 04:49 PMArchie MeadeRe: Inductive Proof
- Aug 2nd 2011, 05:40 PMveronicak5678Re: Inductive Proof
Thanks for the answer, but I don't follow it.

What do you mean by the question marks?

We know n > 3, so 3n^3 > 3*81 - Aug 3rd 2011, 02:01 AMArchie MeadeRe: Inductive Proof
- Aug 3rd 2011, 03:02 AMSwlabrRe: Inductive Proof
- Aug 3rd 2011, 10:47 AMveronicak5678Re: Inductive Proof
Got it. Thanks very much, everyone!