Calculating the Limit of n!^(1/n) and (1/n)(n!)^(1/n)

[jbear12]

The problem is to caculate the limit for:
lim n!^{\frac{1}{n}}

and
lim {\frac{1}{n}} (n!)^{\frac{1}{n}}

Hints to this problem are
the theorem:
lim inf |\frac{Sn+1}{Sn}| \leq lim inf |Sn|^{\frac{1}{n}} \leq lim sup |Sn|^{\frac{1}{n}} \leq lim sup |{\frac{Sn+1}{Sn}}|

and
lim {(1+ {\frac{1}{n}})}^n = e

I really don't have a clue how to solve this, not even how to apply the hint.
Please help! Thanks!

 

[jbear12]

Anyone?

 

[Senjai]

I don't hace an answer to this, but it might be best to learn how to use the forum LaTex editor, it's hard to read your syntax.

wrap your latex code with (tex) and (/tex) (replace the () with [] in your post to make it work), until you get used to using latex, just use the latex equation editor in your post, the latex reference button when posting your post.

 

[jbear12]

Hi Senjai
Can you tell me what's wrong with my code? I spent half an hour editing this and it only displays the first part...I have a midterm tomorrow :(

 

[jbear12]

I mean the hint theorem

 

[jbear12]

it works now :D

 

[jbear12]

anyone?