Help with a limit as n->infinity

Hi guys, I wondered if you could assist me with the following limit...

lim (n -> infinity) (2^{n})/(2^{n + 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!

Re: Help with a limit as n->infinity

Quote:

Originally Posted by

**Shadow236** Hi guys, I wondered if you could assist me with the following limit...

lim (n -> infinity) (2^{n})/(2^{n + 1})

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

So what is the difficulty?

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 2^{n} x 2^{1}, and then the 2's cancel.