You are walking along the x axis and you start at $\displaystyle x = 0$. At each time step you move to $\displaystyle x + 1$ with probability $\displaystyle p = \frac{1}{1+x}$ and to $\displaystyle x-1$ with probability $\displaystyle p = \frac{x}{1+x}$. What is the expected number of steps until you return to 0 for the first time?