# Two sequence be convergent

I'm having trouble on figuring out how to show x_n and y_n are convergent. I get that the last part is Comparison Theorem. So if i can show the two sequences are convergent I can say it's the Comparison Theorem. I'm just not sure how to say both are convergent.

well, $\{x_n\}$ is an increasing sequence which is bounded from above, by $y_1$ for instance (because $x_n<y_n<y_1$ because $\{y_n\}$ is decreasing), and therefore $\{x_n\}$ converges.
similarly, $\{y_n\}$ converges