0
$\begingroup$

enter image description here

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.

$\endgroup$
3
$\begingroup$

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

$\endgroup$
  • $\begingroup$ Ohh i see! That makes sense. Thanks a lot $\endgroup$ – Natasha Epperson Mar 9 '15 at 14:44

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.