MathDB

Romania District Olympiad 2007 - Grade XI

Source:

April 10, 2011

limitinductionreal analysisreal analysis unsolved

Problem Statement

Let

a_1\in (0,1)

and

(a_n)_{n\ge 1}

a sequence of real numbers defined by

a_{n+1}=a_n(1-a_n^2),\ (\forall)n\ge 1

. Evaluate

\lim_{n\to \infty} a_n\sqrt{n}