Stuck on proof by induction

**dtwazere** · October 17th 2010, 08:13 AM

Hey, Stuck on this proof by induction question. I can get so far but not sure where to go after.

$3*2^n < n!$ when $n>4$

Basis for Induction

$3*2^5 < 5!$

$96 < 120$

Induction Step

We assume $3*2^n <n!$ when $n>4$

We need to prove that $3*2^n^+^1 < (n+1)!$

$(n+1)! = (n+1)n!$

$(3*2^n)(n+1)<(n+1)n!$

$(3*2^n)(n+1)<(n+1)!$

This is as far as I can get

Any help would be appreciated!

**tonio** · October 17th 2010, 08:21 AM

Originally Posted by dtwazere

Hey, Stuck on this proof by induction question. I can get so far but not sure where to go after.

$3*2^n < n!$ when $n>4$

Basis for Induction

$3*2^5 < 5!$

$96 < 120$

Induction Step

We assume $3*2^n <n!$ when $n>4$

We need to prove that $3*2^n^+^1 < (n+1)!$

$(n+1)! = (n+1)n!$

$(3*2^n)(n+1)<(n+1)n!$

$(3*2^n)(n+1)<(n+1)!$

This is as far as I can get

Any help would be appreciated!