MathDB

Romania District Olympiad 2004 - Grade XI

Source:

April 10, 2011

limitPutnamreal analysisreal analysis unsolved

Problem Statement

Let

(x_n)_{n\ge 0}

a sequence of real numbers defined by

x_0>0

and

x_{n+1}=x_n+\frac{1}{\sqrt{x_n}}

. Compute

\lim_{n\to \infty}x_n

and

\lim_{n\to \infty} \frac{x_n^3}{n^2}