$\frac{2008}{2009}$ $\ +$ $\frac{2009}{2010}$ $\ +$ $\frac{2010}{2011}$ $\ +$ $\frac{2011}{2008}$
= $\frac{2008}{1}$ $\ +$ $\frac{1}{1}$ $\ +$ $\frac{1}{1}$ $\ +$ $\frac{1}{2008}$
= ( $\frac{2008}{1}$ $\ +$ $\frac{1}{2008}$ ) $\ + 1 + 1$
$\ = 1 + 1 + 1$
$\ = 3$
Vì $\ 3 < 4$
$\ ⇒$ $\frac{2008}{2009}$ $\ +$ $\frac{2009}{2010}$ $\ +$ $\frac{2010}{2011}$ $\ +$ $\frac{2011}{2008}$ $\ < 4$
