Gambling Addiction

Gabe has a crippling gambling addiction. As such, he plays a game where the winning number on the $n$th game, where $n \geq 1$, is uniformly at random selected from the set $\{1,2,\dots, n+2\}$. Let $W$ be the random variable representing how many times Gabe plays before he wins. Find $\mathbb{E}[W]$. If the answer is infinite, answer $-1$.