May 19th, 2013, 01:06 AM  #1 
Newbie Joined: May 2013 Posts: 7 Thanks: 0  Uniform convergence of a serie
My earlier post was about to prove the series is convergent if and divergent if . So now I have got this problem to show the series is uniform convergent as if . If I am trying ti use the Weierstrass Test I get annoyed when I could not continue what to do the next step when it was wrong. Could you please show me what to do? What I did was, . Since is not convergent, the abovementioned series couldn't be uniform convergent. Which is why I did something wrong. 
May 19th, 2013, 08:23 AM  #2  
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: Uniform convergence of a serie Quote:
To prove that is uniformly convergent let us choose some fixed value such that so we have the following . Hence the series is uniformly convergent on  
May 20th, 2013, 06:46 AM  #3  
Newbie Joined: May 2013 Posts: 7 Thanks: 0  Re: Uniform convergence of a serie Quote:
 
May 20th, 2013, 07:33 AM  #4 
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: Uniform convergence of a serie
Hopefully an example will clear the doubt Prove that is uniformly convergent on since we know that is convergent forall , it must be convergent for , right ? So let us now apply the Mtest Hence is uniformly convergent on Now , can we generalize that for 

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convergence, serie, uniform 
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