find the limit of the sequence: (n!) ^ (1/n) as n -> infinity

i don't even know where to start on this one. i think if i get a nod in the right direction i'd be able to get it, so can anyone here give me that nod?

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- November 30th 2007, 04:11 PMbartendorsparkyfind the limit of the sequence
find the limit of the sequence: (n!) ^ (1/n) as n -> infinity

i don't even know where to start on this one. i think if i get a nod in the right direction i'd be able to get it, so can anyone here give me that nod? - November 30th 2007, 06:31 PMTKHunny
It could help to consider

- November 30th 2007, 06:46 PMPaulRS
as

Simply:

Thus: and (this is enough for what you want to know, but do go on)

And:

Then and

So we have

Therefore:

Now if you divide by and take the limit you get that, by the squeeze theorem - December 1st 2007, 02:27 PMThePerfectHacker
Use the following trick.

Let be a seqeuence of non-zero real numbers. If converges then converges to the same thing.