S = $\dfrac{1}{2.3}$ + $\dfrac{1}{3.4}$ +...+$\dfrac{1}{9.10}$
=> S = $\dfrac{1}{2}$ - $\dfrac{1}{3}$ + $\dfrac{1}{3}$ - $\dfrac{1}{4}$ + .....+ $\dfrac{1}{9}$ - $\dfrac{1}{10}$
=> S = $\dfrac{1}{2}$ - $\dfrac{1}{10}$
=> S = $\dfrac{5}{10}$ - $\dfrac{1}{10}$
=> S = $\dfrac{4}{10}$ = $\dfrac{2}{5}$