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: 12,165 Thanks: 472 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: 12,165 Thanks: 472 Math Focus: Calculus/ODEs  Re: Series convergence
Using the integral test, can you now determine for what values of x the following converges: where 

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