# Sepecial "limit sequence"

• Jul 18th 2009, 03:47 AM
dhiab
Sepecial "limit sequence"
• Jul 18th 2009, 07:37 AM
pomp
$\displaystyle \frac{{}^{n} C_k}{n^k} = \frac{n!}{n^k (n-k)! k!} = \frac{n(n-1) \ldots (n-k+1)}{n^k k!}$

Now compare orders of terms in the numerator and denominator. I don't know if you have the answer to work towards, so just to give you a bit more direction here it is if you want it:

Spoiler:
$\displaystyle \frac{1}{k!}$

Hope this helps.
pomp.
• Jul 18th 2009, 08:00 AM
dhiab
Quote:

Originally Posted by pomp
$\displaystyle \frac{{}^{n} C_k}{n^k} = \frac{n!}{n^k (n-k)! k!} = \frac{n(n-1) \ldots (n-k+1)}{n^k k!}$

Now compare orders of terms in the numerator and denominator. I don't know if you have the answer to work towards, so just to give you a bit more direction here it is if you want it:

Spoiler:
$\displaystyle \frac{1}{k!}$

Hope this helps.
pomp.

Hello : Thank you I'have some details :

The numerator is a polyniom :

http://www.mathramz.com/xyz/latexren...7ec91a2b5c.png
Then :
http://www.mathramz.com/xyz/latexren...d276152a2c.png