1
$\begingroup$

Let $\{a_n\},\{b_n\},\{c_n\}$ be sequences of positive real numbers such that $\lim_{n\to\infty}c_n=0$. Is it the case that the sequences

$$ \left\{\frac{a_n-b_n}{a_nc_n}\right\} \qquad\text{ and }\qquad \left\{\frac{a_n-b_n}{b_nc_n}\right\} $$ have the same set of limit points in the extended real line $\mathbb R\cup\{-\infty\}\cup\{\infty\}$?

$\endgroup$

Your Answer

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

Browse other questions tagged or ask your own question.