I try to compute the following limit:
\lim_{n\to\infty}\left(\prod_{k=1}^{n} \binom{n}{k}\right)^\frac{1}{n}
I'm interested in finding some reasonable ways of solving the limit. I don't find any easy approach. Any hint/suggestion is very welcome.
Answer
All the binomial coefficients except the last one are at least n, so the nth root is at least n^{\frac{n-1}{n}}, so the limit is infinity.
No comments:
Post a Comment