Suppose that both series and are absolutely convergent. Show that then so too is the series . Does the converse hold?

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- September 25th 2010, 04:25 PMrondo09Does the converse hold?
Suppose that both series and are absolutely convergent. Show that then so too is the series . Does the converse hold?

- September 25th 2010, 08:30 PMHallsofIvy
Consider .

- September 25th 2010, 10:56 PMchisigma
- September 26th 2010, 02:43 AMHallsofIvy
Yes, the "converse" of "if A then B" is "if B then A".

- September 26th 2010, 05:58 AMchisigma
... very well!... what about and ?... the series converges absolutely... is the same also for ?...

Kind regards

- September 26th 2010, 07:30 AMrondo09
- September 26th 2010, 07:39 AMchisigma
If and absolutely converge then is , so that is or also and the series converges...

Kind regards