Using Sterling's Formula to prove log(n!) = Θ(nlogn)

Asked Oct 22 '19 at 02:14

Active Oct 22 '19 at 02:14

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I'm reviewing a proof here

and I'm having trouble understanding how to get to step 1. I know Sterlings formula is sqrt(2pi*n) * (n/e)^n but where did they get (1 + o(1/n) from in step 1?

asked Oct 22 '19 at 02:14

cplusalex

It appears to be part of the specific form of Stirling's formula they are quoting. – Greg Martin Oct 22 '19 at 02:44
Look at the bottom of https://en.wikipedia.org/wiki/Stirling%27s_approximation#Derivation - although using Stirling is a complete overkill to establish this estimate. – peter a g Oct 22 '19 at 02:44

Using Sterling's Formula to prove log(n!) = Θ(nlogn)

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