Question

How do you use a power series to find the exact value of the sum of the series 1+2+42!+83!+164!+… ?

Answer 1

Unless you're missing a fraction bar somewhere, the sum of that series approaches infinity.

Otherwise, the other option looks like $1 + 2 + \frac{4}{2!} + \frac{8}{3!} + \frac{16}{4!}$

Which has a power series of $\frac{2^{n}}{n!}$, starting at i=0 and going to infinity