Convergence tests for series

Hi I was wondering if anyone could help me with a quick question:

If both and converge and both sums are equal what can you conclude about the two series?

If one of and converges and the other one diverges, which converges and which diverges?

Thanks :)

Re: Convergence tests for series

Quote:

Originally Posted by

**Dragonkiller** Hi I was wondering if anyone could help me with a quick question:

If both

and

converge and both sums are equal what can you conclude about the two series?

If one of

and

converges and the other one diverges, which converges and which diverges?

There is a standard theorem that says: If a series converges absolutely then it converges conditionally.

i.e. If converges then converges.

Now that answers both questions, but how?