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January 29th, 2011, 06:26 AM  #1 
Senior Member Joined: Oct 2010 Posts: 126 Thanks: 0  Divergence and convergence
I'm not sure if I'm heading down the right path here. I'd gladly appreciate some help. 
January 29th, 2011, 10:44 AM  #2 
Senior Member Joined: Nov 2010 Posts: 502 Thanks: 0  Re: Divergence and convergence
Well, we could just come out and sum one. For a geometric series with ratio r (and I will assume WLOG that the first term is 1), Consider S_n = 1 + r + r^2 + r^3 +...+ r^n Then (S_n)r = r + r^2 + r^3 + ... + r^(n+1). Solve for S, and take a limit. 
January 29th, 2011, 05:23 PM  #3  
Senior Member Joined: Oct 2010 Posts: 126 Thanks: 0  Quote:
How does this 'take a limit' concept work? What exactly is meant by without any loss of generality? I still don't get part a.  
January 29th, 2011, 11:35 PM  #4 
Senior Member Joined: Oct 2010 Posts: 126 Thanks: 0  Now and if r < 1, then So If r > 1, and the series does not converge. , provided that r < 1, a Geometric Progression converges to a sum of 

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convergence, divergence 
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