limits again...

lim ( n!(mn)n)1/n
n→∞

4 Answers

33
Abhishek Priyam ·

when such factorials are there take log to convert products to sum, it may help.

33
Abhishek Priyam ·

n!1/n/mn=y
nlogy=logn+log(n-1)+....+1-logm-logn
logy=sum(log(n-r)/n) (r=1ton)

1
Akshay Pamnani ·

1/me is right
(n factorial/npowern)power1/n is equal to 1/e
this is standard limit

341
Hari Shankar ·

Yes, just use Stirling Formula and you are home

Reminds me of http://www.goiit.com/posts/list/differential-calculus-what-is-limit-n-tends-to-infinity-n-1-1010486.htm

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