# Math Help - Sepecial "limit sequence"

1. ## Sepecial "limit sequence"

Calculate :
Knowing :

2. $\frac{{}^{n} C_k}{n^k} = \frac{n!}{n^k (n-k)! k!} = \frac{n(n-1) \ldots (n-k+1)}{n^k k!}$

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

Hope this helps.
pomp.

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

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

Hope this helps.
pomp.
Hello : Thank you I'have some details :

The numerator is a polyniom :

Then :