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April 22nd, 2010, 06:20 AM  #1 
Newbie Joined: Apr 2010 Posts: 16 Thanks: 0  Infinite series : 1/2^(n^2)
Can anyone help me with the sum of this infinite series sigma(1/2^(n^2)) ,n=0,1,2,3...I have calculated the answer to be 2 but my proof is a miserable one.It would be very useful if someone can come up with the right proof.

April 22nd, 2010, 11:06 AM  #2  
Member Joined: Nov 2007 Posts: 50 Thanks: 0  Re: Infinite series : 1/2^(n^2) Quote:
Another thing, which can be easily said about the sum, is that it is not a rational number, since the binary expansion is obviously not periodic.  
April 22nd, 2010, 11:08 AM  #3 
Senior Member Joined: Jun 2009 Posts: 150 Thanks: 0  Re: Infinite series : 1/2^(n^2) and your sum is strictly less, about 1.564468, not 2. The value can be found in terms of Jacobi's Theta function, 
April 22nd, 2010, 10:58 PM  #4 
Newbie Joined: Apr 2010 Posts: 16 Thanks: 0  Re: Infinite series : 1/2^(n^2)
Can you tell me where I can find more about the theta function.I don't quite seem to understand what is given in wikipedia.


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1 or 2n2, infinite, series 
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