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So there's this assignment I'm doing. Let p=1/2. I already proved that for a random walk P(X_n=k) = (n over (n+k)/2) * 2^(-n)
Now I need to prove that lim n->inf (n^(1/2))P(X_2n=2k)) = 1/pi.
Given is stirling's limit. Though I have no idea how to do this.
I'm typing this from my phone and I have no idea how to write in latex, so sorry.