December 29th, 2010, 09:43 PM  #1 
Member Joined: Oct 2010 Posts: 37 Thanks: 0  convergence of series
`For what values of the real number does the following series converge? 
December 30th, 2010, 05:28 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 933 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: convergence of series
Hint 1: use the series expansion of sin. Hint 2: the harmonic series diverges. 
December 30th, 2010, 07:03 AM  #3 
Member Joined: Oct 2010 Posts: 37 Thanks: 0  Re: convergence of series
I get . Then? And it is not a harmonic series. (I think a harmonic series is given by ) 
December 30th, 2010, 07:15 AM  #4  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 933 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: convergence of series Quote:
 
December 30th, 2010, 07:25 AM  #5 
Member Joined: Oct 2010 Posts: 37 Thanks: 0  Re: convergence of series
greater than 3

December 30th, 2010, 08:35 AM  #6  
Senior Member Joined: Nov 2010 Posts: 502 Thanks: 0  Re: convergence of series Quote:
 
December 30th, 2010, 08:35 AM  #7 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 933 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: convergence of series
You're thinking along the right lines, but that would converge to zeta(9)/k + small stuff. Edit: DLowry beat me to it. 
December 30th, 2010, 08:52 PM  #8 
Member Joined: Oct 2010 Posts: 37 Thanks: 0  Re: convergence of series
silly mistake on my part. it diverges when 
December 30th, 2010, 09:00 PM  #9 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 933 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: convergence of series
Ding ding ding, give that man a prize!

January 2nd, 2011, 12:08 PM  #10 
Member Joined: Nov 2010 Posts: 77 Thanks: 0  Re: convergence of series
Hi the sum is < < then when a<=1 the series diverge


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