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Sequence

Source: Chinese Northern Mathematical Olympiad 2007

August 5, 2007
algebra proposedalgebra

Problem Statement

Sequence {an} \{a_{n}\} is defined by a1=2007, an+1=an2an+1 a_{1}= 2007,\, a_{n+1}=\frac{a_{n}^{2}}{a_{n}+1} for n≥1. n \ge 1. Prove that [an]=2007−n [a_{n}] =2007-n for 0≤n≤1004, 0 \le n \le 1004, where [x] [x] denotes the largest integer no larger than x. x.
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