Thread: Help with a limit as n->infinity

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

lim (n -> infinity) (2ⁿ)/(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!

Originally Posted by Shadow236

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

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

So what is the difficulty?

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.