Hello everyone,
So the issue I am having is with the problem:
Determine if the series converges or diverges.
Sum of (-1)^n * (2n+3)!/((3^2n*n)!(n+2)!.

I know that it is the ratio test because of the factorials, and so far I have plugged it into the equation. Not sure what to do with the (-1) and there gets to a certain point where I get stuck. Would just like some clarifiction as to what steps to take to solve this.
Thanks!

Question

Hello everyone, 
So the issue I am having is with the problem:
Determine if the series converges or diverges.
Sum of (-1)^n * (2n+3)!/((3^2n*n)!(n+2)!.

I know that it is the ratio test because of the factorials, and so far I have plugged it into the equation. Not sure what to do with the (-1) and there gets to a certain point where I get stuck. Would just like some clarifiction as to what steps to take to solve this.
Thanks!

perl · Answer

how far did you get

anonymous · Answer

I got to 
$$\lim_{n \rightarrow \infty} (-1)* \frac{ (2n+4) }{ (3^{2n}+1)(n+3) }$$

perl · Answer

so the limit of that is zero

anonymous · Answer

I need some clarification on steps, I just need to know if the limit converges or diverges

perl · Answer

the limit converges because you have an exponential in the denominator (which dominates )

perl · Answer

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