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!

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- Apr 23rd 2012, 09:35 AMkaratekidContinued 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 PMigniteRe: Continued fraction for sqrt(e)
Here you can find proof for continued fraction of $\displaystyle e^\frac{2}{k}$ :

JSTOR:The Simple Continued Fraction Expansion of e