How to Prove Stirling's Formula for ln(n!) ?

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Homework Statement



Prove that ln(n!) = nln(n) - n + ln(2*pi*n)/2 for large n.


Homework Equations



I've been working on the proof but I just can't get it. Can anyone help me out?

The Attempt at a Solution

 

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You can find the proof at many places on the web.
 

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