My Math Forum Limit generalizing

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 October 23rd, 2016, 01:35 PM #1 Newbie   Joined: Oct 2016 From: Czech Republic Posts: 1 Thanks: 0 Limit generalizing I'm confused with this: I need to generalize the formula $\lim_{n\to\infty }\frac{a_n}{b_n}$ = $\frac{\lim_{n\to\infty} a_n}{\lim_{n\to\infty } b_n}$ so that it can be applied even in exceptional cases. I see that the exceptional case is when $b_n=0$. I appreciate all of you help
 October 23rd, 2016, 02:02 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 6,936 Thanks: 2265 Math Focus: Mainly analysis and algebra Can you give some context to this problem?
 October 24th, 2016, 11:13 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 2,633 Thanks: 678 What do you mean by "generalize"? The statement you give should be "As long as $lim_{n\to \infty} a_n$ and $\lim_{n\to\infy} b_n$ exists and the latter limit is not 0, $\lim_{n\to\infty}\frac{a_n}{b_n}= \frac{\lim_{n\to\infty} a_n}{\lim_{n\to\infty} b_n}$."

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