Trying to find a nice way to simplify the question:
Which is bigger 2000! or 1000^2000?
I don't know what kind of reasoning I can apply here.
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1Hint: compare 999*1001 to 1000^2 – Lily Dec 03 '14 at 00:25
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Ah, that does it. I was trying to regroup in different ways but that definitely works, thanks. – Bitmaximus Dec 03 '14 at 00:28
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Don't forget about 2000 :) – Lily Dec 03 '14 at 00:37
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In Factorial Inequality problem $\left(\frac n2\right)^n > n! > \left(\frac n3\right)^n$ it is shown that
$$n!<\left(\frac n2\right)^n.$$ For $n=2000$ we have
$$2000!<\left(\frac {2000}{2}\right)^{2000}=1000^{2000}.$$
