# Help with a limit as n->infinity

• Apr 14th 2013, 10:45 AM
Help with a limit as n->infinity
Hi guys, I wondered if you could assist me with the following limit...

lim (n -> infinity) (2n)/(2n + 1)

At this time the limit is turning out to be (infinity/infinity), which I know is not allowed. For some reason I'm just getting confused with the next step because of the n's in the exponent.
Thanks for the help!
• Apr 14th 2013, 10:57 AM
Plato
Re: Help with a limit as n->infinity
Quote:

Hi guys, I wondered if you could assist me with the following limit...
lim (n -> infinity) (2n)/(2n + 1)

$(\forall n)\frac{2^n}{2^{n+1}}=\frac{1}{2}$

So what is the difficulty?
• Apr 14th 2013, 11:04 AM
Re: Help with a limit as n->infinity
How did you come to that answer? Shouldn't it be infinity/infinity?

EDIT: Nevermind, I've got it. The denominator becomes 2n x 2​1, and then the 2's cancel.