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 March 20th, 2014, 10:01 AM #1 Member   Joined: Mar 2014 Posts: 33 Thanks: 0 Am I using the limit comparison test properly? Hello everyone, So I have an exercise: 5*sqrt(n)/(2n^(3/2) + 5n + 8) Can you tell me if I am applying the limit comparison test correctly? (Also I apologize that I don't know how to put the correct math symbols up yet... if someone could point me in that direction in the process that would be helpful!) Here's what I am doing. I am comparing it with b_n = sqrt(n)/(n^3/2) which is equal to 1/n which is a divergent p-series. Then take (a_n)/(b_n) which, as lim n -> infinity (a_n)/(b_n) = 5/2 which is a number c > 0, therefore since b_n diverges, they both diverge due to part one of the limit comparison test. My main question is: Is my logic and the reasoning behind what I am doing correct? And if it is not, can you tell me what I am doing wrong? Thanks a lot!
 March 20th, 2014, 03:45 PM #2 Senior Member     Joined: Sep 2007 From: USA Posts: 349 Thanks: 67 Math Focus: Calculus Re: Am I using the limit comparison test properly? It is true that $a_n=O(b_n)$ as n approaches infinity. O is the big-O notation. Therefore, if an infinite series of $b_n$ diverges, an infinite series of $a_n$ diverges. If you want to write nice and neat mathematical symbols, you can use Latex. It isn't too difficult to use. Check this link out: http://mymathforum.com/latex.htm. Also, if you want to see how someone on this forum used Latex to display something, you can push the quote button and see the Latex code they used. There is another way to get Latex code for something. Maxima, a free computer algebra system, is capable of copying results to the clipboard as Latex. You can then paste it in. I haven't had the need to do it yet, though.

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