2021 Fall AMC 12B Problems/Problem 18
Revision as of 17:46, 24 November 2021 by Concavetriangle (talk | contribs) (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...")
Set 
, and for 
let 
be determined by the recurrence ![\[u_{k+1} = 2u_k - 2u_k^2.\]](http://latex.artofproblemsolving.com/4/d/2/4d293888df7007ec4ada4b226a235ad82caf9d9f.png)
This sequence tends to a limit; call it 
. What is the least value of 
such that ![\[|u_k-L| \le \frac{1}{2^{1000}}?\]](http://latex.artofproblemsolving.com/6/c/d/6cdccfccc047b6c8985ceea4d5d27e3bc9e4bab3.png)
