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

Decide whether the series below is absolutely convergent, conditionally convergent, or divergent:

[tex]\sum_{1}^{\infty}(2n+3)!/(n!)^2[/tex]

3. The attempt at a solution

By graphing the equation, I am confident that the series is divergent, but I don't know how to prove it. I cannot do the algebraic manipulation for a ratio test, assuming it is even possible, and none of the other tests seem applicable. Since it's apparently going to be divergent, I can't to a comparison test.

That leaves either a straight limit test, or a limit comparison test. Unfortunately, it looks to me like the limit converges to zero. Factorial is stronger than the power function, but how can I prove factorial squared isweakerthan a larger factorial in the numerator?

Thanks :)

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# Homework Help: Proof of Divergence?

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