MathDB

sequence

Source: Ukraine 1997 grade 10

July 21, 2009

algebra proposedalgebra

Problem Statement

A sequence is defined by a_1\equal{}a_2\equal{}a_3\equal{}1 and a_{n\plus{}3}\equal{}\minus{}a_n\minus{}a_{n\plus{}1} for all

n \in \mathbb{N}

. Prove that this sequence is not bounded , i.e. that for every

M \in \mathbb{R}

there is an

n

for which

|a_n|>M.