S= S = $\frac{1}{2.3}$ + $\frac{1}{3.4}$ + $\frac{1}{4.5}$ + ... + $\frac{1}{19.20}$
= $\frac{1}{2}$ - $\frac{1}{3}$+ $\frac{1}{3}$ - $\frac{1}{4}$+$\frac{1}{4}$ - $\frac{1}{5}$ + ... - $\frac{1}{19}$ + $\frac{1}{20}$
= $\frac{1}{2}$ - $\frac{1}{20}$
= $\frac{9}{20}$