Continued fraction for sqrt(e)

• Apr 23rd 2012, 09:35 AM
karatekid
Continued fraction for sqrt(e)
Hi all,

Can anyone point me towards a proof that the continued fraction expansion of sqrt(e) is [1,1,1,1,5,1,1,9,1,1,13...] (ie. a proof that the pattern continues)? I can find plenty for e itself but none for the square root.

Thanks!
• Apr 23rd 2012, 04:04 PM
ignite
Re: Continued fraction for sqrt(e)
Here you can find proof for continued fraction of $e^\frac{2}{k}$ :
JSTOR:The Simple Continued Fraction Expansion of e
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