Question 63
Determine if there are polynomials $p(x)$ and $q(x)$ with real coefficients such that
$$
\frac{p(n)}{q(n)} = 1 + \frac{1}{2!} + \frac{1}{3!} + \dots + \frac{1}{n!}
$$
for every positive integer $n$.
$$
\frac{p(n)}{q(n)} = 1 + \frac{1}{2!} + \frac{1}{3!} + \dots + \frac{1}{n!}
$$
for every positive integer $n$.