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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