What's the limit of $(1+\frac{1}{8^n})^n$ What's the limit of $(1+\frac{1}{8^n})^n$? How do I find the answer for this?
Thanks in advance. 

It might be useful to let $L=\lim_{n\to\infty} \left(1+\frac{1}{8^n}\right)^n$ and then notice that $\ln(L)=\lim_{n\to\infty}n\cdot\ln\left(1+\frac{1}{8^n}\right)$. Because $\ln(\cdot)$ is a continuous function, we can do that.  Then, you might be able to solve it from there.
