Math Help - Quick question on series

If I know that a series

is convergent. Is it not possible to further deduce that


Hjörtur

Originally Posted by hjortur

If I know that a series

is convergent. Is it not possible to further deduce that


Hjörtur

The implication in the other direction is straightforward: it's the Ratio Test:

Ratio Test - ProofWiki

Does that help at all?

I just wanted to be sure, I am pretty sure that the limit must hold.
What if for all n. What happens to the limit then? Undefined?

Originally Posted by hjortur

I just wanted to be sure, I am pretty sure that the limit must hold.
What if for all n. What happens to the limit then? Undefined?

Looks like it to me. The ratio test definitely holds in the other direction (as I've said) but you've found a counterexample such that the way you stated it does *not* hold.

Then i'll just assume that particular series is not 0. Thanks