MathDB

Algebra expressions

Source: Archimedes Junior 2009

March 17, 2020

algebra

Problem Statement

Consider the numbers

A= \frac{1}{4}\cdot \frac{3}{6}\cdot \frac{5}{8}\cdot ...\frac{595}{598}\cdot \frac{597}{600}

and

B= \frac{2}{5}\cdot \frac{4}{7}\cdot \frac{6}{9}\cdot ...\frac{596}{599}\cdot \frac{598}{601}

. Prove that: (a)

A < B

, (b)

A < \frac{1}{5990}