Hey math'ers,

I have $\displaystyle I_k= \left( \ln \left( 1+{k}^{-1} \right) \right) ^{k} $, where k goes towards infinity...

I know the answer is supposed to be ln e = 1.

I would think $\displaystyle {k}^{-1} $ goes towards $\displaystyle 0 $, which means the expression inside $\displaystyle \ln $ would go towards $\displaystyle 1 $, so $\displaystyle \ln $ goes towards $\displaystyle 0 $ and the power of $\displaystyle k $ would just speed up the process.

What am I doing wrong?

Any help is appreciated...

Simon DK