# Another quick series question

• Oct 2nd 2009, 03:28 PM
hjortur
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?
• Oct 2nd 2009, 03:45 PM
Plato
Quote:

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?
• Oct 2nd 2009, 03:50 PM
hjortur
Yeah, sorry, I noticed now that I deleted "if series is convergant" when I was formatting the message

Fixed
• Oct 2nd 2009, 04:39 PM
Plato
• Oct 2nd 2009, 05:06 PM
hjortur
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.