Question

If f^ (n)(0) = (n + 1)! for n = 0, 1, 2, find the Maclaurin series for f

Answer 1

\[f(x)=\sum_{n=0}^\infty \frac{f^{(n)}(0)}{n!}x^n=\sum_{n=0}^\infty \frac{(n+1)!}{n!}x^n=\cdots\]Surely you know how to simplify factorial expressions?