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April 28th, 2012, 10:17 PM  #21 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Convergence and Divergence's
We just need for the magnitude of each successive term to decrease at a certain critical rate or beyond to get a convergent series, regardless of how large the first terms are.

April 29th, 2012, 05:46 PM  #22  
Senior Member Joined: Jan 2010 Posts: 324 Thanks: 0  Re: Convergence and Divergence's Quote:
Is this the formula?  
April 29th, 2012, 07:31 PM  #23 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Convergence and Divergence's
No, that formula (I think you mean ) is used in the ratio test, which was inconclusive on the series. I found the sum using the computer...I bet our friend Zardoz could show how to manually find it. 
April 29th, 2012, 07:37 PM  #24 
Senior Member Joined: Jan 2010 Posts: 324 Thanks: 0  Re: Convergence and Divergence's
You know about him? 
April 29th, 2012, 07:42 PM  #25 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Convergence and Divergence's
Yes, our resident analyst and I go waaaay back. 
April 29th, 2012, 07:43 PM  #26 
Senior Member Joined: Jan 2010 Posts: 324 Thanks: 0  Re: Convergence and Divergence's
It really is a boys club, aye?

April 29th, 2012, 07:50 PM  #27 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Convergence and Divergence's
Unfortunately...yes. :P 
April 30th, 2012, 08:03 PM  #28  
Senior Member Joined: Jan 2010 Posts: 324 Thanks: 0  Re: Convergence and Divergence's Quote:
I cannot seem to follow it in the book  
April 30th, 2012, 08:22 PM  #29 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs  Re: Convergence and Divergence's
By simple inspection we can tell that diverges, and the use of the limit comparison test would really be redundant. 

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