MathDB

2011 PUMaC Individual Finals A2

Source:

September 24, 2019

algebra

Problem Statement

Define the sequence of real numbers

\{x_n\}_{n \geq 1}

, where

x_1

is any real number and

x_n = 1 - x_1x_2\ldots x_{n-1} \text{ for all } n > 1.

Show that

x_{2011} > \frac{2011}{2012}