Alternating series convergence or divergence $\sum\limits_{k=1}^\infty \frac{(-1)^n n^2}{(n+1)^2}$

Question

$$\sum_{k=1}^\infty \frac{(-1)^n n^2}{(n+1)^2}$$

The ratio test came up inconclusive, and I don't know where to go from there.

score 3 · Answer 1 · answered May 09 '16 at 15:05

3

Sequence limit not equal to zero, so divergence theorem.

answered May 09 '16 at 15:05

student forever

Okay thanks! So the limit would equal 1 using L'Hopitals? – nal.10 May 09 '16 at 15:07
1

Limit doesn't exist, but the limit of absolute value is $1$. Not necessary to take L'h, dividing $n^2$ both numerator and denominator is enough. – student forever May 09 '16 at 15:09

1 Answers1