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257

Part of 1953 Moscow Mathematical Olympiad

Problems(1)

MMO 257 Moscow MO 1953 x_n=(x^2_{n-1}+2)/(2x_(n-1))

Source:

8/9/2019
Let x0=109x_0 = 10^9, xn=xn−12+22xn−1x_n = \frac{x^2_{n-1}+2}{2x_{n-1}} for n>0n > 0. Prove that 0<x36−2<10−90 < x_{36} - \sqrt2 < 10^{-9}.
recurrence relationSequenceinequalitiesalgebra