A stochastic process $\{x_{k}\mid k=1,2,3,...\}$ of zeroes and ones is given with the property that $x_1 = 1, x_2 = 0$ and for every $k>2$ it is true that the probability of the event $x_k = 1$ is equal to $\frac {1}{k-1} \sum_{i=1} ^{k-1} x_i$.
What is the probability of the event $\sum_{i=1}^{n} x_i=k$ for $1 \le k \le n-1$?
I literally have no idea how to begin this problem. Any suggestions would be helpful.
Maybe I can look at complementary event, but other than that I'm lost.