Unless you're missing a fraction bar somewhere, the sum of that series approaches infinity.
Otherwise, the other option looks like [tex]1 + 2 + \frac{4}{2!} + \frac{8}{3!} + \frac{16}{4!} [/tex]
Which has a power series of [tex] \frac{2^{n}}{n!} [/tex], starting at i=0 and going to infinity
