# Questions about sequences

## Homework Statement

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

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.

## Answers and Replies

tiny-tim
Science Advisor
Homework Helper
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" [Broken]

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

Last edited by a moderator:
Well thank you for your prompt answer. I hope you don't mind but I have another question.
$$\sum_{k=1}^{\infty} \frac {1} {k(k+1)}$$
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
$$\frac {k} {k+1}$$
but webassign is telling me that it is the wrong answer. Can anyone help, it would be grealty appreciated.

SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
Expand using partial fractions: $$\frac{1}{k(k+1)}=\frac{\,A\,}{k}+\frac{B}{k+1}$$

Find A & B.

jhae2.718
Gold Member
By boundedness, are there certain values which the values of the sequence never get larger (an upper bound) or smaller (a lower bound) than?

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
$$\lim_{n \rightarrow \infty} ne^{-n/2} = 0$$
Thank you so much for your help.