Convergence of alternating series

• Jan 14th 2010, 01:31 PM
Cairo
Convergence of alternating series
Any ideas for the attached?
• Jan 14th 2010, 01:41 PM
HallsofIvy
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
• Jan 14th 2010, 02:07 PM
Cairo
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?
• Jan 14th 2010, 03:21 PM
Drexel28
Quote:

Originally Posted by Cairo
Any ideas for the attached?

Clearly, it is not going to be uniformly convergent, since for any $x\in\mathbb{R}$ we eventually have that $\frac{1}{2n}\leqslant\frac{1}{n+2x^2}$.
• Jan 25th 2010, 01:41 PM
Cairo
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?