My text book states that: $$\sum_n 2^nx^n=\frac{1}{1-2x}$$ However this doesn't look obvious to me and I would like to prove it, but I don't know how. Could someone help me?
Background: This "formula" appears in the process of finding the generating funcion of the sequence given by: $a_n=\{ \frac{2^n}{n} \}$