Can anyone show the following:

$\displaystyle N^N$$\displaystyle e^{-N}$ $\displaystyle \leq$ $\displaystyle e^{-1}$ x N! $\displaystyle \leq$ N x $\displaystyle N^N$$\displaystyle e^{-N}$

N.B. The "x" are multiplication signs

Printable View

- May 5th 2010, 06:55 AMMathman87Can anyone show this exponential proof?
Can anyone show the following:

$\displaystyle N^N$$\displaystyle e^{-N}$ $\displaystyle \leq$ $\displaystyle e^{-1}$ x N! $\displaystyle \leq$ N x $\displaystyle N^N$$\displaystyle e^{-N}$

N.B. The "x" are multiplication signs - May 5th 2010, 10:28 AMTikoloshe
Use Stirling’s approximation.

- May 5th 2010, 04:47 PMMathman87
I dont know how to use that? could you show me how its done?