$\frac{1}{2.3}$ + $\frac{1}{3.4}$ + $\frac{1}{4.5}$ + ... + $\frac{1}{9.10}$
= $\frac{1}{2}$ - $\frac{1}{3}$ + $\frac{1}{3}$ - $\frac{1}{4}$ + $\frac{1}{4}$ - $\frac{1}{5}$ + ... + $\frac{1}{9}$ - $\frac{1}{10}$
= $\frac{1}{2}$ - $\frac{1}{10}$ = $\frac{2}{5}$