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. 

Hint: Use the Binomial Theorem:
$$(1+8^{-n})^n=\sum_{k=0}^n 8^{-nk}\binom nk = 1 + 8^{-n}\left(\sum_{k=1}^n 8^{-n(k-1)}\binom nk\right)$$
and the identity $\displaystyle\binom nk = \binom{n-1}{k-1}+\binom{n-1}k$ to estimate the parenthesized sum.

NB. Logarithms (as Steven Stadnicki suggests) provide an easier solution, but perhaps you don't have them available yet.
