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Is x_50000<1? [ILL 1971]

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January 1, 2011
calculusintegrationreal analysisalgebra proposedalgebra

Problem Statement

A sequence of real numbers x1,x2,…,xnx_1,x_2,\ldots ,x_n is given such that xi+1=xi+1300001−xi2, i=1,2,…,x_{i+1}=x_i+\frac{1}{30000}\sqrt{1-x_i^2},\ i=1,2,\ldots , and x1=0x_1=0. Can nn be equal to 5000050000 if xn<1x_n<1?
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