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This fit very badly with the surrounding text. (I have qualms about including this so early in the article as well.) |
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The number can be represented by an infinite series of [[Egyptian fractions]], with denominators defined by 2<sup>n</sup>th terms of a [[Fibonacci]]-like recurrence relation a(n)=34a(n-1)-a(n-2), a(0)=0, a(1)=6. <ref>https://oeis.org/A082405</ref>
:<math>\sqrt{2}=\frac{3}{2}-\frac{1}{2}\sum_{n=0}^\infty \frac{1}{a(2^n)}=\frac{3}{2}-\frac{1}{2}\left(\frac{1}{6}+\frac{1}{204}+\frac{1}{6930}+\frac{1}{235416}+\dots \right) </math>
==Continued fraction representation==
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