MathDB

17th ibmo - el salvador 2002./q5.

Source: Spanish Communities

April 14, 2006

inductionalgebra unsolvedalgebra

Problem Statement

The sequence of real numbers

a_1,a_2,\dots

is defined as follows:

a_1=56

and

a_{n+1}=a_n-\frac{1}{a_n}

for

n\ge 1

. Show that there is an integer

1\leq{k}\leq2002

such that

a_k<0

.

Back to Problems View on AoPS