Help with a limit as n->infinity

**Shadow236** · Apr 14th 2013, 09:45 AM

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!

**Plato** · Apr 14th 2013, 09:57 AM

Originally Posted by Shadow236

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

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

So what is the difficulty?

**Shadow236** · Apr 14th 2013, 10:04 AM

How did you come to that answer? Shouldn't it be infinity/infinity?

EDIT: Nevermind, I've got it. The denominator becomes 2ⁿ x 2¹, and then the 2's cancel.

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