Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Given $\lim \limits_{n\to \infty}\frac{a_n}{b_n}=1$

is this claim $\lim \limits_{n\to \infty}(a_n-b_n)=0$ false or true?

I think it's false because I can't talk about $\lim \limits_{n\to \infty}a_n$ nor about $\lim \limits_{n\to \infty}b_n$ however, I can't find an example that will disprove the claim.

Thank you.

share|cite|improve this question
up vote 5 down vote accepted

Hint: try a quotient of polynomials of the same degree.

share|cite|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

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