You could try the root test...
Root test - Wikipedia, the free encyclopedia
SUM, from 1 to infinity of:
ln(n)
________
(n+1)^3
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.
Or:
Is there another test that should be performed next?
You could try the root test...
Root test - Wikipedia, the free encyclopedia
No, it doesn't. The ratio test acually tells you that this series converges absolutely:
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?
Oops, yes, you are right (obviously I didn't even take the time to read carefully enough what I had written myself).
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 .