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June 3rd, 2018, 05:29 PM   #1
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Math analysis

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 June 3rd, 2018, 06:11 PM #2 Senior Member   Joined: Aug 2012 Posts: 1,972 Thanks: 550 What do you think about the first one? Just give us your thoughts, don't even edit yourself. Just think about the problem, what it's asking, why it might or might not be true. Is your language Portuguese? I speak a little Spanish. To me, Portuguese is sort of like Spanish and nothing at all like Spanish at the same time. It's like I "should" be able to understand it but a lot of times I can't. Thanks from Roberto 37 Last edited by Maschke; June 3rd, 2018 at 06:25 PM.
June 4th, 2018, 02:49 PM   #3
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I tried to translate in Google, do you understand?
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Last edited by skipjack; June 5th, 2018 at 06:34 AM.

June 4th, 2018, 03:23 PM   #4
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Quote:
 Originally Posted by Roberto 37 I tried to translate in Google, do you understand?
What do you think about the first one? Just give us your thoughts, don't even edit yourself. Just think about the problem, what it's asking, why it might or might not be true.

Last edited by skipjack; June 5th, 2018 at 06:35 AM.

 June 4th, 2018, 05:15 PM #5 Newbie   Joined: Jun 2018 From: Brasil Posts: 3 Thanks: 0 I think the letter c is correct; options I and II true. Last edited by skipjack; June 5th, 2018 at 06:35 AM.
 June 4th, 2018, 08:52 PM #6 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,344 Thanks: 2466 Math Focus: Mainly analysis and algebra #MeToo Thanks from Roberto 37
 July 12th, 2018, 08:19 AM #7 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 In general, as long as two sequences, $\displaystyle \{an\}$, $\displaystyle \{bn\}$, have finite sums, it is true that $\displaystyle \lim_{n\to\infty} (a_n+ b_n)= \lim_{n\to\infty} a_n+ \lim_{n\to\infty} b_n$. $\displaystyle \lim_{n\to\infty} (a_n- b_n)= \lim_{n\to\infty} a_n- \lim_{n\to\infty} b_n$ $\displaystyle \lim_{n\to\infty} (a_n)(b_n)= (\lim_{n\to\infty} a_n)(\lim_{n\to\infty} b_n)$. $\displaystyle \lim_{n\to\infty}\frac{a_n}{b_n}= \frac{\lim_{n\to\infty} a_n}{\lim_{n\to\infty}}$ (As long as $\displaystyle \lim_{n\to\infty}$ is not 0.) From that, it follows immediately that options I and II are true. As for III, I have no idea where "2" might have come from! The limit of $\displaystyle \frac{a_n}{a_n}$ is 1, not 0.

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