MathDB

a combinatorial inequality

Source: ISI Bstat Entrance, 2006

March 1, 2012

inequalitiesinductionalgebra unsolvedalgebra

Problem Statement

for any positive integer

n

greater than

1

, show that

2^n<\binom{2n}{n}<\frac{2^n}{\prod\limits_{i=0}^{n-1} \left(1-\frac{i}{n}\right)}