June 3rd, 2018, 06:29 PM  #1 
Newbie Joined: Jun 2018 From: Brasil Posts: 20 Thanks: 0  Math analysis
Can someone please help? Iam Brazil

June 3rd, 2018, 07:11 PM  #2 
Senior Member Joined: Aug 2012 Posts: 2,098 Thanks: 601 
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. Last edited by Maschke; June 3rd, 2018 at 07:25 PM. 
June 4th, 2018, 03:49 PM  #3 
Newbie Joined: Jun 2018 From: Brasil Posts: 20 Thanks: 0 
I tried to translate in Google, do you understand?
Last edited by skipjack; June 5th, 2018 at 07:34 AM. 
June 4th, 2018, 04:23 PM  #4 
Senior Member Joined: Aug 2012 Posts: 2,098 Thanks: 601  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 07:35 AM. 
June 4th, 2018, 06:15 PM  #5 
Newbie Joined: Jun 2018 From: Brasil Posts: 20 Thanks: 0 
I think the letter c is correct; options I and II true.
Last edited by skipjack; June 5th, 2018 at 07:35 AM. 
June 4th, 2018, 09:52 PM  #6 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,508 Thanks: 2513 Math Focus: Mainly analysis and algebra 
#MeToo

July 12th, 2018, 09:19 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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