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SOS-Stirling's formula!!!

mathmari
in Homework Help

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Hello!!! Could anyone help me to solve this exercise?

 

Using Stirling's formula show that( see the first attached file stirling1!!!), where S(x)=-xlnx-(1-x)ln(1-x), 0<=x<=1.

I used n!=e^(-n)n^(n+1/2)(2π)^(1/2)*(1+O(1/n)) and my result is (see the second attached file stirling2).

Is this equal to the result i have to show??

 

Thank you!!!!

post-90061-0-58930700-1364741960.png

post-90061-0-54375200-1364741970.png

Edited by mathmari

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