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

For which values of a does this series converge?

[tex]\sum[/tex] (n!)^2/(an)!

3. The attempt at a solution

I know a cannot be a negative integer because you cannot have a negative factorial.

If a is 0, then it's limit is infinity. ie. lim (n!)^2/ 0 = infinity

If a is +1, then lim cn+1/cn = ((n+1)!)^2/(n+1)! x n!/(n!)^2

= lim (n+1)^2/(n+1) = lim (n+1)/1 = infinity

For the series to converge it's limit from n to infinity must be equal to 0 right? So is there any value of a where it converges, or is my math wrong?

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# Homework Help: For which values of a does this series converge?

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