Inequality with e, factorial, exponential function...

Hi!

Could you help me prove this inequality?

When I try induction , I get:

and this is when I have no idea how to get . Could I ask for a small hint? It cannot be that hard to prove :)

Or maybe you have another, more constructive way to prove this inequality?

Re: Inequality with e, factorial, exponential function...

Quote:

Originally Posted by

**wilhelm** Hi!

Could you help me prove this inequality?

When I try induction , I get:

and this is when I have no idea how to get [latex](n+1)^{n+2}[/latex]. Could I ask for a small hint? It cannot be that hard to prove :)

Or maybe you have another, more constructive way to prove this inequality?

Made an oopsie! (Headbang)

-Dan

Re: Inequality with e, factorial, exponential function...

Dan, I have found the inequality is correct for and provided a proof by induction on another site.

For example, for , we have:

and for we have:

-Mark

Re: Inequality with e, factorial, exponential function...

Quote:

Originally Posted by

**MarkFL2** Dan, I have found the inequality is correct for

and provided a proof by induction on another site.

For example, for

, we have:

and for

we have:

-Mark

I worked out a few on my calculator for convenience and used "e" instead of Exp. (Doh)

Thanks for the catch.

-Dan