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#1
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Re: Convergence/Divergence
#2 is extremely convergent, but it's possible to squeeze it to something that meets your property, but doesn't have limit 0. You can squeeze it to (2n-1)^n/(2n)^n, which is "a bunch of numbers all less than 1 being multiplied out", but converges to e^-1/2.
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#2
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Re: Convergence/Divergence
if we want better asymptotics in 2, write it as
(2n)!/(2^{2n} n^n n!) ~ \sqrt{2}*e^{-n} by Stirling. |
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