The Number e

Compounding without limit

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• $e = \lim (1 + 1/n)^n \approx 2.71828$.
• $e = \sum \frac{1}{k!}$, and $e^x$ is its own derivative.
• Continuous growth at rate $r$: $A = A_0 e^{rt}$.

Steps

1. Generous bank
2. Approaching e
3. e
4. Sum the series
5. Mixed-up hats
6. Continuous compounding