Limits as n goes to infinity

1. Apr 4, 2012

TranscendArcu

1. The problem statement, all variables and given/known data

3. The attempt at a solution
So I know that the limit as $n → ∞$ of $(1 - \frac{1}{n})^n = \frac{1}{e}$. Using this information, is it legitimate to observe:

The limit as $n → ∞$ of $(1 - \frac{1}{n})^{n ln(2)} =$ the limit as $n → ∞$ of $((1 - \frac{1}{n})^n)^{ln(2)} = e^{-1 ln(2)} = e^{ln(\frac{1}{2})} = \frac{1}{2}$

2. Apr 4, 2012

Robert1986

Looks good to me.

3. Apr 4, 2012

Dick

Looks ok to me.