Approximations and Stirling's formula
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The following are demonstrated:
1) ln(n!) = nlnn + O(n)
2) ln(n!) ~= nlnn - n
3) n! ~= sqrt(2*pi*n) * n^n * e^-n
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Solution Summary
This shows how to make approximations involving n!
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Stirling's Approximation
1) Now area under the curve < area under the steps < area of the rectangle
hence
2) Now taking the area under the curve to be approximately the ...
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