Difference between revisions of "2021 Fall AMC 12B Problems/Problem 18"
(Created page with "Set <math>u_0 = \frac{1}{4}</math>, and for <math>k \ge 0</math> let <math>u_{k+1}</math> be determined by the recurrence <cmath>u_{k+1} = 2u_k - 2u_k^2.</cmath> This sequenc...") |
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+ | ==Problem== | ||
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Set <math>u_0 = \frac{1}{4}</math>, and for <math>k \ge 0</math> let <math>u_{k+1}</math> be determined by the recurrence <cmath>u_{k+1} = 2u_k - 2u_k^2.</cmath> | Set <math>u_0 = \frac{1}{4}</math>, and for <math>k \ge 0</math> let <math>u_{k+1}</math> be determined by the recurrence <cmath>u_{k+1} = 2u_k - 2u_k^2.</cmath> | ||
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<math>(\textbf{A})\: 10\qquad(\textbf{B}) \: 87\qquad(\textbf{C}) \: 123\qquad(\textbf{D}) \: 329\qquad(\textbf{E}) \: 401</math> | <math>(\textbf{A})\: 10\qquad(\textbf{B}) \: 87\qquad(\textbf{C}) \: 123\qquad(\textbf{D}) \: 329\qquad(\textbf{E}) \: 401</math> | ||
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+ | ==Solution== |
Revision as of 17:48, 24 November 2021
Problem
Set , and for
let
be determined by the recurrence
This sequence tends to a limit; call it . What is the least value of
such that