MathDB

Sequence 1994

Source: IMO Shortlist 1994, A1

December 26, 2006

Sequencerecurrence relationalgebraIMO Shortlist

Problem Statement

Let a_{0} \equal{} 1994 and a_{n \plus{} 1} \equal{} \frac {a_{n}^{2}}{a_{n} \plus{} 1} for each nonnegative integer

n

. Prove that 1994 \minus{} n is the greatest integer less than or equal to

a_{n}

0 \leq n \leq 998