[SOLVED] Monotone Sequence

**vinson24** · April 18th 2010, 02:38 PM

Using $A_{n+1}/A_n$
$[ne^{-n}]_{n=1}$
ive got to
$\frac {(n+1)e^{-(n+1)}}{ne^{-n}}$
but dont know how to simplify from there

**CaptainBlack** · April 18th 2010, 10:33 PM

Originally Posted by vinson24

Using $A_{n+1}/A_n$
$[ne^{-n}]_{n=1}$
ive got to
$\frac {(n+1)e^{-(n+1)}}{ne^{-n}}$
but dont know how to simplify from there

Please repost this with a clearer explanation.

CB

**vinson24** · April 19th 2010, 04:50 AM

$ne^{-n}$ is the sequence n=1 to infinity
and they want me to find out if its strictly increasing or strictly decreasing using ratio of successive terms

I have gotten this far $\frac {(n+1)e^{-(n+1)}}{ne^{-n}}$
but not sure how to simplify this to show that this is greater or less than 1. I know the answer is strictly decreasing but not sure how to simply the ratio to prove that

**CaptainBlack** · April 19th 2010, 05:29 AM

Originally Posted by vinson24

$ne^{-n}$ is the sequence n=1 to infinity
and they want me to find out if its strictly increasing or strictly decreasing using ratio of successive terms

I have gotten this far $\frac {(n+1)e^{-(n+1)}}{ne^{-n}}$
but not sure how to simplify this to show that this is greater or less than 1. I know the answer is strictly decreasing but not sure how to simply the ratio to prove that

$\frac {(n+1)e^{-(n+1)}}{ne^{-n}}=\frac{(n+1)e^{-1}}{n}=e^{-1}+\frac{e^{-1}}{n}$

CB

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