My Math Forum  

Go Back   My Math Forum > College Math Forum > Real Analysis

Real Analysis Real Analysis Math Forum


Reply
 
LinkBack Thread Tools Display Modes
April 22nd, 2010, 05:20 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.
Zeefinity is offline  
 
April 22nd, 2010, 10:06 AM   #2
Member
 
Joined: Nov 2007

Posts: 50
Thanks: 0

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

Quote:
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.
kompik is offline  
April 22nd, 2010, 10:08 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,
g_edgar is offline  
April 22nd, 2010, 09:58 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.
Zeefinity is offline  
Reply

  My Math Forum > College Math Forum > Real Analysis

Tags
1 or 2n2, infinite, series



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Infinite series clandarkfire Calculus 6 November 6th, 2011 03:23 AM
Infinite series : 1/r^r Zeefinity Real Analysis 4 August 28th, 2011 11:18 PM
Infinite Series WannaBe Calculus 3 January 7th, 2010 01:27 AM
Infinite series johnny Calculus 1 September 9th, 2009 05:57 AM
Infinite Series Mathforum1000 Abstract Algebra 0 December 31st, 1969 04:00 PM





Copyright © 2019 My Math Forum. All rights reserved.