Question

How to find Limit ((1/2n)*log(2nCn)), where n tends to infinity?

Answer 1

\[\lim_{n \rightarrow \infty} \frac{ 1 }{ 2n }\ln(2nCn)\]

Answer 2

Sorry, made a typo...\[\lim_{n\to\infty}\frac{\ln(C(2n,n))}{2n}=\lim_{n\to\infty}\frac{1}{2n}\ln\left[\frac{(2n)!}{n!(2n-n)!}\right]\]

Answer 3

At any point, do you get
\[\lim_{n\to\infty}\frac{1}{2n}\left[\sum_{k=0}^\infty\ln2+\sum_{k=1}^\infty \ln (2n-2k+1)\right]\]