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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It obviously does, 2n! grows faster than n!^2 – mtheorylord Nov 03 '17 at 10:50
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@mtheorylord Which means that it diverges. But you're technically right: any sequence converges or not:) – skyking Nov 03 '17 at 10:52
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Related : https://math.stackexchange.com/questions/1606836/why-does-this-series-sum-n-0-infty-fracn22n-converge/1606870 – Arnaud D. Nov 03 '17 at 11:30
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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
aleden
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