If a series is

$\displaystyle

a_n > 0 \quad \text{ for every } n

$

And converges must there be a N such that ?

$\displaystyle

\frac{a_{n+1}}{a_n} < 1 \quad \text{ for every } n\geq N

$

Does this hold in general?

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- Oct 2nd 2009, 03:28 PMhjorturAnother quick series question
If a series is

$\displaystyle

a_n > 0 \quad \text{ for every } n

$

And converges must there be a N such that ?

$\displaystyle

\frac{a_{n+1}}{a_n} < 1 \quad \text{ for every } n\geq N

$

Does this hold in general? - Oct 2nd 2009, 03:45 PMPlato
- Oct 2nd 2009, 03:50 PMhjortur
Yeah, sorry, I noticed now that I deleted "if series is convergant" when I was formatting the message

Fixed - Oct 2nd 2009, 04:39 PMPlato
- Oct 2nd 2009, 05:06 PMhjortur
I was just having a trouble with one proof on my assignment.

If the statement from my post were true it would have made my life a heck of a lot easier.

Well, after thinking about this I concluded that this was indeed false.

But it doesn't matter, I figured out how to write my proof using the limit

comparison test.

I am not going to post the question here, I am not sure about my

university's standpoint on asking for help with homework on this forum.

Thanks for the link