 My Math Forum Using limit comparison with negative numbers?

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 April 21st, 2016, 08:21 PM #1 Member   Joined: May 2015 From: Earth Posts: 64 Thanks: 0 Using limit comparison with negative numbers? So i'm looking at an answer sheet to an old exam, and it's asking for me to prove that the sum of (-n)/(2n^2+5) converges or diverges. They use limit comparison in the answer. Everywhere I look says that the parts in the sum must be greater than 0, yet the answer sheet seems to say differently? It gives ( (-n)/(2n^2+5) )/( -1/n ) as n --> infinity as the setup to the problem. Does the fact that this fraction is not negative make this okay? These series are killing me and nothing really makes sense. April 21st, 2016, 08:56 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,696 Thanks: 2681 Math Focus: Mainly analysis and algebra $$\sum_{n=1}^\infty {-n \over 2n^2+5} = -\sum_{n=1}^\infty {n \over 2n^2 + 5}$$ So the sum on the left hand side converges if and only if the sum on the right hand side converges. April 21st, 2016, 09:14 PM #3 Member   Joined: May 2015 From: Earth Posts: 64 Thanks: 0 That's helpful, but that's not what was written in the answer key. I understand why it was okay for them to change use the negative signs in their work, since they cancel out, but is that the only reason it's acceptable? Still seems weird. April 21st, 2016, 09:26 PM #4 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,696 Thanks: 2681 Math Focus: Mainly analysis and algebra Yes, they are using $-\frac1x$ because the negatives cancel out to give a finite limit greater than zero which is the definition of the test. Personally, I would say it's more correct to do the transformation above on both series to make the terms positive, and then run the test. Last edited by v8archie; April 21st, 2016 at 09:44 PM. April 22nd, 2016, 11:38 AM #5 Member   Joined: May 2015 From: Earth Posts: 64 Thanks: 0 Okay that makes a lot more sense, thank you!! Tags comparison, limit, negative, numbers Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post mathdisciple Calculus 1 March 20th, 2014 03:45 PM zaff9 Calculus 1 April 18th, 2013 07:05 AM chapsticks Calculus 1 June 23rd, 2012 08:41 PM fuzzwaz Calculus 3 November 5th, 2011 03:34 PM AdamL Calculus 4 April 5th, 2008 04:39 PM

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