4. The infinite simple continued fraction expansion of the number $e$ is
$$e=[2 ; 1,2,1,1,4,1,1,6,1,1,8, \ldots]$$
a) Find the first eight convergents of the continued fraction of $e$.
b) Find the best rational approximation to $e$ having a denominator less than 100.
4. a) $\frac{2}{1}, \frac{3}{1}, \frac{8}{3}, \frac{11}{4}, \frac{19}{7}, \frac{87}{32}, \frac{106}{39}, \frac{193}{71}$
b) $\frac{193}{71}$