I have a question regarding the following problem:
Describe if the following series converges absolutely, conditionally or diverges.
Sigma (n=2 to infinity) (-1)^n * (n^2+2n)/(n^3-3n))
Using the "absolute" ratio test, I get lim = 1, so no conclusion can be drawn.
Using the "absolute" limit comparison test with 1/n, I get lim = 1, concluding that it diverges. (as 1/n diverges)
Using the alternating series test this series a) is decreasing and b) the limit goes to 0; concluding that this series converges.
As the absolute part of the series diverges by the limit comparison test, but the absolute part of the series converge by the alternating series test, can I conclude this series converges conditionally?