Questions about sequences

  • #1

Homework Statement


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

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.
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,836
251
Welcome to PF!

Hi Barbados_Slim! Welcome to PF! :smile:

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

"monotonic" means that it only goes one way …

either it never decreases, or it never increases …

see http://en.wikipedia.org/wiki/Monotonic" [Broken]:wink:

I don't know what "boundedness" means … it seems rather vague. :redface:
 
Last edited by a moderator:
  • #3
Well thank you for your prompt answer. I hope you don't mind but I have another question.
[tex]
\sum_{k=1}^{\infty} \frac {1} {k(k+1)}
[/tex]
is an example of a telescoping series. Find a a formula for the general term [itex]S_n[/itex] of the sequence of partial sums.
I've reached the conclusion that the formula for the general term is
[tex]
\frac {k} {k+1}
[/tex]
but webassign is telling me that it is the wrong answer. Can anyone help, it would be grealty appreciated.
 
  • #4
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,394
1,045
Expand using partial fractions: [tex]\frac{1}{k(k+1)}=\frac{\,A\,}{k}+\frac{B}{k+1}[/tex]

Find A & B.
 
  • #5
jhae2.718
Gold Member
1,170
20
By boundedness, are there certain values which the values of the sequence never get larger (an upper bound) or smaller (a lower bound) than?
 
  • #6
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
[tex]
\lim_{n \rightarrow \infty} ne^{-n/2} = 0
[/tex]
Thank you so much for your help.
 

Related Threads on Questions about sequences

  • Last Post
Replies
9
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
3
Views
4K
  • Last Post
Replies
6
Views
4K
Replies
2
Views
170
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
10
Views
4K
Top