SUM, from 1 to infinity of:
I work this out using the ratio test for convergence and the answer I get is "1"...
Does this sound right?
If so, this then means that there are no other tests that can be done correct? The test is simply inconclusive.
Is there another test that should be performed next?
The first factor goes to 1 as n goes to , since
and the second factor goes to 0.
No: if the ratio test fails, the root test might still be used to prove absolute convergence.If so, this then means that there are no other tests that can be done correct?
Maybe it was because I was already quite sure that the series converges. (Why? - Because I know that converges and can be used to bound the given series from above.)
Sure, in that case, the ratio test does not decide the question of convergence vs. divergence.If a ratio test of series = 1 , it means nothing .