Problem

Source: Tuymaada 2000 Juniors 4

Tags: algebra, inequalities, three variable inequality



Prove that if the product of positive numbers $a,b$ and $c$ equals one, then $\frac{1}{a(a+1)}+\frac{1}{b(b+1)}+\frac{1}{c(c+1)}\ge \frac{3}{2}$