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May 6th, 2013, 11:55 PM  #1 
Member Joined: Mar 2013 Posts: 56 Thanks: 0  Convergence and divergence
Hallo all! I am struggling with these questions, so a solution would be very helpful for my revision! (E is the sigma symbol) A) Infinity E = [(6)^(m+1)]/[4^(5m)] n =0 B) Infinity E = [cos^2 (pi*n/]/[n sqrt(n)] n=0 C) infinity E = [4+cos(n)]/4^n n=0 please and thank you! 
May 7th, 2013, 12:58 AM  #2 
Member Joined: Jan 2012 Posts: 80 Thanks: 0  Re: Convergence and divergence
Is the question whether the series diverge or converge? If so the first one can be shown to converge using the ratio test: We need to find the limit: As this is less than 1 we can say the series converges. 
May 7th, 2013, 01:38 AM  #3 
Member Joined: Jan 2012 Posts: 80 Thanks: 0  Re: Convergence and divergence
For the second one the term is undefined at n=0. Did you mean: 
May 7th, 2013, 02:03 AM  #4 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: Convergence and divergence [color=#000000]1. so the series converges. 2. so the series converges. 3. so the series converges.[/color] 
May 7th, 2013, 03:24 PM  #5 
Member Joined: Mar 2013 Posts: 56 Thanks: 0  Re: Convergence and divergence
thank you zardoz!

May 9th, 2013, 09:24 PM  #6 
Member Joined: Dec 2010 From: Miami, FL Posts: 96 Thanks: 0  Re: Convergence and divergence
Zardoz is a beast. It is worth pointing out however, that is a nontrivial fact. If I were your grader, I would not give full credit. lol. 
May 10th, 2013, 12:37 AM  #7  
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,989 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: Convergence and divergence Quote:
 
May 10th, 2013, 12:59 AM  #8  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Convergence and divergence Quote:
 
May 10th, 2013, 11:30 PM  #9 
Member Joined: Dec 2010 From: Miami, FL Posts: 96 Thanks: 0  Re: Convergence and divergence
Ooooh. It is indeed. I thought it was the sequence . Of course, everything is trivial if you use logarithms and L'Hopital's rule. 

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