Question 100
An infinite sequence satisfies $x_1=1$ and, for every positive integer $k$,
$$x_{2k}=-x_k,\qquad x_{2k-1}=(-1)^{k+1}x_k.$$
Prove $x_1+\cdots+x_n\ge0$ for every positive integer $n$.
$$x_{2k}=-x_k,\qquad x_{2k-1}=(-1)^{k+1}x_k.$$
Prove $x_1+\cdots+x_n\ge0$ for every positive integer $n$.