Hello, jjtjp!

Here's the problem:

So I use ratio test (obviously):

. We are taking absolute values; drop the (-1)^n.

After some cancellations I have:

It seems that I could say that cancels,

but then again, n + 1 will increase faster than n. . This is not true.

I can't figure out where to go from here though. .Thanks!

We have: .

Divide numerator and denominator by

. .

Therefore: .