Very classical inequatily with natural numbers
Source: Canada 1998
March 4, 2006
inequalitiesinequalities unsolved
Problem Statement
Let be a natural number such that . Show that
\frac {1}{n \plus{} 1} \left( 1 \plus{} \frac {1}{3} \plus{} \cdot \cdot \cdot \plus{} \frac {1}{2n \minus{} 1} \right) > \frac {1}{n} \left( \frac {1}{2} \plus{} \frac {1}{4} \plus{} \cdot \cdot \cdot \plus{} \frac {1}{2n} \right).