
Real Analysis Real Analysis Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: 1,990 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: 1,990 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. 

Tags 
convergence, divergence 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Convergence and divergence  math221  Calculus  3  April 8th, 2013 06:39 AM 
Convergence and Divergence's  FreaKariDunk  Real Analysis  28  April 30th, 2012 08:22 PM 
Divergence and convergence  MathematicallyObtuse  Algebra  3  January 29th, 2011 10:35 PM 
Maple and Convergence/Divergence  Gotovina7  Calculus  0  February 14th, 2008 06:28 PM 
Show convergence/divergence.  Noworry  Calculus  0  December 31st, 1969 04:00 PM 