Iterating a Square-Root Expression
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This Demonstration shows an iteration of the sequence , starting with the initial value
,
; the conditions avoid complex numbers. The sequence converges to
for all permissible values of
. The sequence is monotonically increasing, decreasing, or constant, according to whether
,
, or
.
Contributed by: Omran Kouba (June 2016)
Open content licensed under CC BY-NC-SA
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Note that the equation or
has the positive solution
.
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