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Find integer

Source: China Western Mathematical Olympiad 2012 P6

September 29, 2012
limitlogarithmsalgebra proposedalgebra

Problem Statement

Define a sequence {an}\{a_n\} bya0=12, an+1=an+an22012,(n=0, 1, 2, ⋯ ),a_0=\frac{1}{2},\ a_{n+1}=a_{n}+\frac{a_{n}^2}{2012}, (n=0,\ 1,\ 2,\ \cdots), find integer kk such that ak<1<ak+1.a_{k}<1<a_{k+1}.
(September 29, 2012, Hohhot)
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