# Thread: Another quick series question

1. ## Another 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?

2. Originally Posted by hjortur
If a series is
$\displaystyle a_n > 0 \quad \text{ for every } n$
Is there a N such that ?
$\displaystyle \frac{a_{n+1}}{a_n} < 1 \quad \text{ for every } n\geq N$
Does this hold in general?
This may well be a problem in language or translation.
I don’t know what the above quote means.
Consider this, $\displaystyle a_n=\frac{1}{n}$ satisfies that condition.
So what exactly does you question mean?

3. Yeah, sorry, I noticed now that I deleted "if series is convergant" when I was formatting the message

Fixed

4. 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