IMO 1971 LL USS48

A sequence of real numbers x1, x2, . . . , xn is given such that

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IMO 1971 LL USS48

Origin: USS

Problem

A sequence of real numbers x1, x2, . . . , xn is given such that xi+1 = xi + 30000 1 −x2 i , i = 1, 2, . . ., and x1 = 0. Can n be equal to 50000 if xn < 1?