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 November 4th, 2014, 10:04 AM #1 Member   Joined: Oct 2013 Posts: 38 Thanks: 2 How do I know when to use the Limit Comparison Test over Direct Comp. Test? If I have An = 2 / root(n^2 - 3), Bn = 1/n I assume that I would probably use the LCT, instead of the direct test, but why couldn't I just use the direct test? is the 2 in the numerator that much of a factor in the long run? More so than the -3, or -4, or whatever it was that would make the number bigger? The distinction of when to use one over the other is confusing me right now. November 4th, 2014, 11:49 AM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,675 Thanks: 2655 Math Focus: Mainly analysis and algebra The 2 makes no difference to me. $$a_n = \frac{2}{\sqrt{n^2 - 3}} \gt \frac2n \gt \frac1n = b_n \qquad n \gt 1$$ November 4th, 2014, 11:55 AM #3 Math Team   Joined: Jul 2011 From: Texas Posts: 3,002 Thanks: 1588 in the case where you might have $\displaystyle a_n = \frac{2}{\sqrt{n^2+3}}$ , you cannot do a direct comparison with $\displaystyle \frac{2}{n}$ since $\displaystyle \frac{2}{\sqrt{n^2+3}} < \frac{2}{n}$ ... in which case, use the limit comparison test. Tags comp, comparison, direct, limit, test 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 02:45 PM chapsticks Calculus 1 June 23rd, 2012 07:41 PM fuzzwaz Calculus 3 November 5th, 2011 02:34 PM jens.w Calculus 2 November 26th, 2008 11:55 AM AdamL Calculus 4 April 5th, 2008 03:39 PM

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