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April 28th, 2012, 08:52 PM  #1 
Senior Member Joined: Feb 2010 Posts: 324 Thanks: 0  Convergence and Divergence's
1. Using the nth term test Diverges right? because (How do I do the arrows in latex?) 
April 28th, 2012, 09:03 PM  #2 
Senior Member Joined: Nov 2011 Posts: 595 Thanks: 16  Re: Convergence and Divergence's
Yes of course it diverges, if the sequence does not go to zero, it diverges. I think you can do an arrow with \rightarrow

April 28th, 2012, 09:08 PM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,208 Thanks: 516 Math Focus: Calculus/ODEs  Re: Convergence and Divergence's
Use n\to\infty to get The limit comparison test also shows it diverges. 
April 28th, 2012, 09:08 PM  #4 
Senior Member Joined: Feb 2010 Posts: 324 Thanks: 0  Re: Convergence and Divergence's
So the the r would be 2/3? I dont think that its right...

April 28th, 2012, 09:11 PM  #5 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,208 Thanks: 516 Math Focus: Calculus/ODEs  Re: Convergence and Divergence's
You would have : edit: Is that the series you meant to give in your first post...now your use of the root test makes more sense. 
April 28th, 2012, 09:12 PM  #6 
Senior Member Joined: Feb 2010 Posts: 324 Thanks: 0  Re: Convergence and Divergence's
and the a would be one.

April 28th, 2012, 09:14 PM  #7 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,208 Thanks: 516 Math Focus: Calculus/ODEs  Re: Convergence and Divergence's
You would have: You could write the series as: 
April 28th, 2012, 09:16 PM  #8 
Senior Member Joined: Feb 2010 Posts: 324 Thanks: 0  Re: Convergence and Divergence's
This one also converges? because i have a/1r is 1/3<1

April 28th, 2012, 09:17 PM  #9 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,208 Thanks: 516 Math Focus: Calculus/ODEs  Re: Convergence and Divergence's
This diverges because . That formula works only for .

April 28th, 2012, 09:19 PM  #10 
Senior Member Joined: Feb 2010 Posts: 324 Thanks: 0  Re: Convergence and Divergence's
Then whats the deal with this formula... a/1r? I thought i had to use that for convergence and divergence, but i can just go off of the r? 

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