Determine whether or not the following sequence converges $$(2n)!\over{(n!)^2}$$ Please help me with which method i need to use to prove this


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  • $\begingroup$ It obviously does, 2n! grows faster than n!^2 $\endgroup$ – mtheorylord Nov 3 '17 at 10:50
  • $\begingroup$ @mtheorylord Which means that it diverges. But you're technically right: any sequence converges or not:) $\endgroup$ – skyking Nov 3 '17 at 10:52
  • $\begingroup$ Related : math.stackexchange.com/questions/1606836/… $\endgroup$ – Arnaud D. Nov 3 '17 at 11:30

This is actually the binomial coefficient of $2n$ and $n$, which clearly does not approach any defined value. See this post:

prove that $\frac{(2n)!}{(n!)^2}$ is even if $n$ is a positive integer


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