December 29th, 2010, 10:43 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, 06:28 AM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 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, 08:03 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, 08:15 AM  #4  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: convergence of series Quote:
 
December 30th, 2010, 08:25 AM  #5 
Member Joined: Oct 2010 Posts: 37 Thanks: 0  Re: convergence of series
greater than 3

December 30th, 2010, 09:35 AM  #6  
Senior Member Joined: Nov 2010 Posts: 502 Thanks: 0  Re: convergence of series Quote:
 
December 30th, 2010, 09:35 AM  #7 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 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, 09:52 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, 10:00 PM  #9 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 937 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, 01:08 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


Tags 
convergence, series 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Series convergence  math221  Calculus  2  April 19th, 2013 03:14 AM 
Series convergence  FreaKariDunk  Real Analysis  3  May 1st, 2012 08:13 PM 
convergence of series  vasudha  Calculus  4  March 9th, 2012 09:23 AM 
Convergence of a series  elimax  Real Analysis  6  July 13th, 2011 03:17 AM 
convergence of series  mghg13  Algebra  1  December 31st, 1969 04:00 PM 