Question

Does this series converge BY THE (LIMIT) COMPARISON TEST?:
http://www.tiikoni.com/tis/view/?id=f503de2

Answer 1

I'm thinking no because not all terms are nonnegative.

Answer 2

despite being able to compare it to (-1)^n /n.

Answer 3

So, this/these test(s) is/are not applicable?

Answer 4

it converges because it does, but not "by the limit comparison test" which, i am fairly sure, is only applicable if the terms are all positive

Answer 5

It also doesn't converge by the regular comparison test, right?

Answer 6

in converges because it is alternating, and the only thing you need to check for an alternating series is if the terms go to zero, but limit comparison test is not used in this example

Answer 7

Yes, I know about the alternating series. I just want to make sure that neither of the comparison tests work for this. (You only mentioned the LIMIT comparison test.)

Answer 8

that is because that is what the question asked

Answer 9

The regular comparison test doesn't work either for the same reason (not all terms of the series are nonnegative), right?

Answer 10

comparison test is for positive terms also , so i guess you cannot use that one either

Answer 11

so yes, you are right

Answer 12

Yay. :)

Answer 13

I have related mini-problems, but I'll post them in their own section/threads. Thanks!

Answer 14

yw