
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: 7,271 Thanks: 2435 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: 2,737 Thanks: 1387 
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  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Am I using the limit comparison test properly?  mathdisciple  Calculus  1  March 20th, 2014 02:45 PM 
Limit Comparison Test  chapsticks  Calculus  1  June 23rd, 2012 07:41 PM 
Comparison Test/Limit Comparison Test Questions  fuzzwaz  Calculus  3  November 5th, 2011 02:34 PM 
A question about the Limit comparison test  jens.w  Calculus  2  November 26th, 2008 11:55 AM 
Limit Comparison Test  AdamL  Calculus  4  April 5th, 2008 03:39 PM 