real analysis - Show that $(x_n)$ convergent to 0

Show that if $x_n \geq 0$ and the limit of $((-1)^nx_n)$ exists, then $(x_n)$ convergent to 0.

I don't have a single clue to solve the problem. I have looking back about monotone sequence, Cauchy sequence, and bounded one, but seem don't lead to this. Please help. Regards

Answer

Since $a_n\ge 0$ we have, $a_n = |(-1)^n a_n|$. If a sequence converges to L then its absolute value convergers to |L|, due to the continuity of the absolute value function.

In your case $L=0$ due to the oscillation of $(-1)^n a_n.$