And here's my proof. Because I don't want to repeatedly type this, and I don't do anything with it for a while, let . Also, assume there is a in front of each of these.
And here's my proof. Because I don't want to repeatedly type this, and I don't do anything with it for a while, let . Also, assume there is a in front of each of these.
Spoiler:
Rewrite this expression as
Using Stirling's approximation , the above equals
your final answer is correct but you need to be more careful with using the approximation
I got the approximation of when tends to infinty , using Riemann Sum
which equals to what redsoxfan325 mentioned .
I believe the is correct but i'm not sure if the above is a rigorous proof .
Well the equals sign is pushing it. In your Riemann sum step what you really mean as that as increases without bound . You of course knew that, but in case anyone misinterpreted it.