Prove the following using the principle of mathematic induction.

n! > n^2, for all integers n >= 4.

I am especially having trouble with the inductive step. Thanks for your help.

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- Oct 29th 2012, 06:01 PMWalshyHelp with a proof by induction
Prove the following using the principle of mathematic induction.

n! > n^2, for all integers n >= 4.

I am especially having trouble with the inductive step. Thanks for your help. - Oct 29th 2012, 06:06 PMProve ItRe: Help with a proof by induction
- Oct 29th 2012, 06:09 PMWalshyRe: Help with a proof by induction
Basis Step: 4!>4^2, 24>16 - that works.

Inductive step: Assume k! >k^2

Goal: (k+1)! > (k+1)^2

= k+1(k!) > k^2+2k+1

stuck here. - Oct 29th 2012, 06:15 PMProve ItRe: Help with a proof by induction
The way you set out these problems needs work - you need to start on one side of your statement and go through a series of arguments to get to the other side. But anyway, your logic is right at least...

$\displaystyle \displaystyle \begin{align*} ( k + 1 ) ! &= (k + 1)k! \\ &> (k + 1)k^2 \\ &> (k + 1)^2 \textrm{ since } k^2 > k + 1 \end{align*}$

It's up to you to prove $\displaystyle \displaystyle \begin{align*} k^2 > k + 1 \end{align*}$ in our region :)