(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Investigate the convergence of the following series.

(2n)!/(n!n!)

3. The attempt at a solution

Number one, I don't see how they get that

if a_{n}= (2n)!, then a_{n+1}= ((2n+2))!, it should be (2n+1)!

Number two, I don't see how they go to the second step, why is the second step not:

(n!n!(2n+2)!)/((n+1)!(n+1)!(2n)!)? why do they have that extra (2n)! in the numerator?

Number three, I don't see why n!n! cancels in the numerator in step 3.

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# Homework Help: Ratio test for infinite series

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