Re: Inductive proof
- To: mathgroup at smc.vnet.net
- Subject: [mg37899] Re: Inductive proof
- From: "Kevin J. McCann" <kjm@KevinMcCann>
- Date: Mon, 18 Nov 2002 00:53:14 -0500 (EST)
- References: <ar7vvt$s76$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
I am not sure what you are really trying to do. An inductive proof is
probably not the way to go.
FindRoot[3^n==n!,{n,4,7}]
gives an answer of about 6.016. An examination of the slope of the two
curves shows that each is monotonically increasing, and n! has the larger
positive slope. If you use Stirling's approximation for the factorial, you
can get a better functional feel for it. If you take the log of the two
terms you compare n Log[3] with n Log[n]-n (Stirling's approx for log n!) it
is clear that the latter is increasing faster.
Kevin
"Sam" <skapoor2 at hotmail.com> wrote in message
news:ar7vvt$s76$1 at smc.vnet.net...
> Hi:
>
> Can anyone help me solve this by induction
>
> 3 to the power n < n!, when n is > 6
>
> Thanks:
>
> -Sam
>
>