 My Math Forum Comparison, Limit Comparison, and Splitting Sums.

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 April 7th, 2013, 01:09 PM #1 Newbie   Joined: Jan 2013 Posts: 26 Thanks: 0 Comparison, Limit Comparison, and Splitting Sums. I'm not really sure when each of these should be done. In fact, I don't really understand the reason that we use the limit comparison test. ?1/(n^2+1) So here I can simply say that P=2>1, so the original converges. ?1/N^3+N^2 Here, I would say that P=3>1, implying the original converges. But my solutions tell me that here I should use a limit comparison with 1/N^3, where the limit ---->N is = 1. So why did I do this? What did I prove by finding the limit that I didn't prove by just comparing directly? What is different in this that I had to use a limit comparison instead of direct? Just the added N^2? I don't understand why. And I also see that when I have some questions that have similar sums to the one directly above me, they just split the sum and evaluate the p series of both sums to find the divergence; is this an alternative to a limit comparison test as well? Thank you, guys. April 18th, 2013, 07:05 AM #2 Math Team   Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus Re: Comparison, Limit Comparison, and Splitting Sums. [color=#000000]For the first one since , , so the series converges. For the second one here is another way, you can compute the result by doing the following .[/color] Tags comparison, limit, splitting, sums 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 chapsticks Calculus 1 June 23rd, 2012 08:41 PM fuzzwaz Calculus 3 November 5th, 2011 03:34 PM jens.w Calculus 2 November 26th, 2008 12:55 PM AdamL Calculus 4 April 5th, 2008 04:39 PM

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