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Hello!!! Could anyone help me to solve this exercise?
Using Stirling's formula show that( see the first uploaded image), 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 uploaded image). Is this equal to the result i have to show??