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
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A100943:
Decimal expansion of the
infinitely nested radical , where
is
Euler’s number.
-
This number is the positive solution from
to the equation
, 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
. One can easily verify that
(1 − y) 2 − (1 − y) = (1 − 2 y + y 2 ) − (1 − y) = y 2 − y = e |
.