May 1st, 2012, 05:59 PM  #1 
Senior Member Joined: Jan 2010 Posts: 324 Thanks: 0  Series convergence then after some integration lim (from b to infint) (3/b+3)=1 so since the integration of 3/n^2 from one to infinity converges then the summation of infinity n=1 3/n^2 would converge? 
May 1st, 2012, 06:45 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 462 Math Focus: Calculus/ODEs  Re: Series convergence
Yes. We have Now, since we may state: If then the series converges. So, we compute: Hence, by the integral test, the series converges. 
May 1st, 2012, 06:55 PM  #3 
Senior Member Joined: Jan 2010 Posts: 324 Thanks: 0  Re: Series convergence
YEY! 
May 1st, 2012, 07:13 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 462 Math Focus: Calculus/ODEs  Re: Series convergence
Using the integral test, can you now determine for what values of x the following converges: where 

Tags 
convergence, series 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Series convergence  math221  Calculus  2  April 19th, 2013 02:14 AM 
convergence of series  vasudha  Calculus  4  March 9th, 2012 08:23 AM 
Convergence of a series  elimax  Real Analysis  6  July 13th, 2011 02:17 AM 
COnvergence of a Series  realanalysisfail  Real Analysis  2  December 14th, 2010 11:15 AM 
convergence of series  mghg13  Algebra  1  December 31st, 1969 04:00 PM 