Prove:
Limit as n --> infinity
n/(n^2+3n+1) -->0
I just don't know how to start here. What algebraic property can I use to get started?
Will this work?
|n/(n^2 +3n + 1)| < | n/(n^2 +3n)| < | n/(n^2)| = 1/n?
Thanks.
I assume from your title, and the fact that this thread is posted in a pretty advanced sub-forum, that you wish to formally prove the statement
.
To do this, the epsilon-delta definition is in order.
The statement means that for each , there exists a [tex]M>0[/tex] such that whenever .
In your case, it is not difficult to see that for any a number can be found such that
whenever
This implies that the limit is ,in fact, 0.
For the proof of , just take values of which are less than some number .
Yes, I do and thanks. I was primarily looking for a way to get started, and I can fill in all the formalities. This is my first analysis class, so all responses are extremely useful, and somewhat ease the frustration of taking such a tedious class.
Thanks everyone!