Confounding Compounding Interest
At first glance, the limit (1 + 1/N)^N for large N seems like it should approach 1, but it actually approaches the number e. Why is this? The approach taken removes focus on the above expression and instead looks at a family of curves, (1 + x/N)^N, and their behavior when N becomes large to tease out the true reason for the seemingly unintuitive tendency towards the number e.
