1. ## [SOLVED] Monotone Sequence

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

2. Originally Posted by vinson24
Using $\displaystyle A_{n+1}/A_n$
$\displaystyle [ne^{-n}]_{n=1}$
ive got to
$\displaystyle \frac {(n+1)e^{-(n+1)}}{ne^{-n}}$
but dont know how to simplify from there
Please repost this with a clearer explanation.

CB

3. $\displaystyle ne^{-n}$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 $\displaystyle \frac {(n+1)e^{-(n+1)}}{ne^{-n}}$
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

4. Originally Posted by vinson24
$\displaystyle ne^{-n}$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 $\displaystyle \frac {(n+1)e^{-(n+1)}}{ne^{-n}}$
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
$\displaystyle \frac {(n+1)e^{-(n+1)}}{ne^{-n}}=\frac{(n+1)e^{-1}}{n}=e^{-1}+\frac{e^{-1}}{n}$

CB