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November 10th, 2013, 10:03 AM  #1 
Newbie Joined: Oct 2013 Posts: 18 Thanks: 0  1st year math  Riemann zeta function & series
the riemann zeta function is defined for p > 1 as prove by considering so my thoughts: as then we just use the definition of convergence to prove that the partial sum converges to 1 and we're done however I'm having troubles trying to show that for some epsilon there exists a real number H s.t. P>H and N>H implies I've tried using geometric series for the inside sum and then trying to rearrange for P or N but to no avail  any help please 
November 10th, 2013, 12:42 PM  #2 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Re: 1st year math  Riemann zeta function & series
Have you noticed that: 
November 10th, 2013, 01:28 PM  #3  
Newbie Joined: Oct 2013 Posts: 18 Thanks: 0  Re: 1st year math  Riemann zeta function & series Quote:
 
November 10th, 2013, 01:42 PM  #4 
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Re: 1st year math  Riemann zeta function & series
If you rearrange into geometric series: Then, each sums to: Does that help? 
November 10th, 2013, 01:58 PM  #5  
Newbie Joined: Oct 2013 Posts: 18 Thanks: 0  Re: 1st year math  Riemann zeta function & series Quote:
 
November 10th, 2013, 02:20 PM  #6  
Senior Member Joined: Jun 2013 From: London, England Posts: 1,316 Thanks: 116  Re: 1st year math  Riemann zeta function & series Quote:
 
November 11th, 2013, 11:21 AM  #7 
Newbie Joined: Oct 2013 Posts: 18 Thanks: 0  Re: 1st year math  Riemann zeta function & series
I'm sorry but I think you misunderstood what I was asking: I'm asking, how do I show that for all there exists a real number H s.t. P>H and N>H implies 

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1st, function, math, riemann, series, year, zeta 
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