Find, as function of $\displaystyle x$, the sum of the infinite series and state its interval of convergence.

$\displaystyle x - 2x^2 + 4x^3 - 8x^4 + ... + (-1)^n 2^n x^{n+1} + ...$

Hey, I hope this is the right board..

How would I determine the answer? I think it's a combination of power series, (like $\displaystyle e^x$ + another series or something like that) but I'm just guessing.

Thanks.