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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
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Re: Infinite series : 1/2^(n^2)

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 Originally Posted by Zeefinity 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.
The claim that the sum is equal to 2 is obviously wrong, since ; and your is a subseries of this series, hence the sum must be smaller.
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. Tags 1 or 2n2, infinite, series Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post clandarkfire Calculus 6 November 6th, 2011 04:23 AM Zeefinity Real Analysis 4 August 29th, 2011 12:18 AM WannaBe Calculus 3 January 7th, 2010 02:27 AM johnny Calculus 1 September 9th, 2009 06:57 AM Mathforum1000 Abstract Algebra 0 December 31st, 1969 04:00 PM

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