What is a monotonic sequence and how do you determine its boundedness?

[Barbados_Slim]

Homework Statement

Determine whether the sequence with the given nth term is monotonic. Find the boundedness of the sequence.
<br /> a_n = ne^{-n/2} <br />

Homework Equations

I don't know

The Attempt at a Solution

I have absolutely no idea what a monotonic sequence is or how to find the boundedness of a sequence. I've tried researching it but I'm still confused. Any help would be greatly appreciated.

 

[tiny-tim]

Welcome to PF!

Hi Barbados_Slim! Welcome to PF!

(try using the X² icon just above the Reply box )

"monotonic" means that it only goes one way …

either it never decreases, or it never increases …

see http://en.wikipedia.org/wiki/Monotonic"

I don't know what "boundedness" means … it seems rather vague.

 

[Barbados_Slim]

Well thank you for your prompt answer. I hope you don't mind but I have another question.
<br /> \sum_{k=1}^{\infty} \frac {1} {k(k+1)}<br />
is an example of a telescoping series. Find a a formula for the general term S_n of the sequence of partial sums.
I've reached the conclusion that the formula for the general term is
<br /> \frac {k} {k+1}<br />
but webassign is telling me that it is the wrong answer. Can anyone help, it would be grealty appreciated.

 

[SammyS]

Expand using partial fractions: \frac{1}{k(k+1)}=\frac{\,A\,}{k}+\frac{B}{k+1}

Find A & B.

 

[jhae2.718]

By boundedness, are there certain values which the values of the sequence never get larger (an upper bound) or smaller (a lower bound) than?

 

[Barbados_Slim]

I figured out the problem with the telescoping series. I was just using the wrong letter, I used "k" instead of "n". As for the other problem about the boundedness. I believe that boundedness refers to certain values that the sequence never gets larger or smaller than, like jhae2.718 said. The graph of the function doesn't appear to be bounded but I got the wrong answer when I said that the bounds do not exist. I think the answer might be zero because
<br /> \lim_{n \rightarrow \infty} ne^{-n/2} = 0<br />
Thank you so much for your help.