Growing

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Prove that $(1 + \frac{1}{n})^n \leq e < 3$.

Which is larger:

(a) $1.000001^{1000000}$ or $2$?

(b) $100^{300}$ or $300!$ (i.e. 300 factorial)?

Published July 2000.