MathNet 2011 Question 4

A sequence $x_1,x_2,\ldots$ is defined by $x_1=1$, $x_{2k}=-x_k$, and $x_{2k-1}=(-1)^{k+1}x_k$ for every $k\ge1$. Prove that $x_1+x_2+\ldots+x_n\ge0$ for every $n\ge1$.