Oliver Grant

Euclid's proof that there are infinitely many primes is famous, but I want to understand it deeply. Assume $p_1, p_2, \ldots, p_n$ are all the primes. Consider $N = p_1 p_2 \cdots p_n + 1$. Then $N$ is either prime or has a prime factor not in our list, contradiction.

I need to derive the Maclaurin series for $f(x) = e^x$ from first principles for my AP Calculus BC exam. I know the formula is: $$f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!} (x-a)^n$$