I'm trying to evaluate what compound interest approaches when the number of compound periods approaches infinity. That is, I'm interested in analytically evaluating Euler's number $e$:
$$\lim_{m \to \infty} \left(1 + \frac{1}{m}\right)^m$$
Do you have any suggestions or ideas regarding how I can approach evaluating this? Also, is there a general approach to solving this kind of limit?