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Template:Sequence of the Day for May 22

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Intended for: May 22, 2013

Timetable

  • First draft entered by Alonso del Arte on March 23, 2012
  • Draft reviewed by Daniel Forgues on May 13, 2012; May 21, 2015
  • Draft to be approved by April 22, 2013
Yesterday's SOTD * Tomorrow's SOTD

The line below marks the end of the <noinclude> ... </noinclude> section.



A100943: Decimal expansion of the infinitely nested radical , where
e
is Euler’s number.
2.222870229721...
This number is the positive solution from
y =
1 ±
2  1 + 4 e
2
to the equation
y 2  −  y  −  e = 0
, the other solution being
1  −  y =  − 1.222870229721...
, which has the same fractional part (so to speak, since those numbers are transcendental). By looking at the infinitely nested surd, it is trivial to see that
y 2  −  y = e
. One can easily verify that
(1  −  y) 2  −  (1  −  y) = (1  −  2 y  +  y 2 )  −  (1  −  y) = y 2  −  y = e
.