# Thread: Convergence of alternating series

1. ## Convergence of alternating series

Any ideas for the attached?

2. To determine absolute convergence, use the ratio test. To determine pointwise convergence, determine for what values of the the absolute value of the terms of the sequence are decreasing. To determine uniform convergence, use the fact that a series converges uniformly on any closed and bounded interval on which it is point wise convergent

3. I didn't think to use the ratio test. I assumed that I would have had to use the Alternating Series Test.

How would this work then?

4. Originally Posted by Cairo
Any ideas for the attached?
Clearly, it is not going to be uniformly convergent, since for any $\displaystyle x\in\mathbb{R}$ we eventually have that $\displaystyle \frac{1}{2n}\leqslant\frac{1}{n+2x^2}$.

5. I'm still trying to prove absolute convergence, but am convinced that the series diverges.

I've used the Comparison test, and noted that 1/n+2x^2 > 1/n.

Is it okay to do this?