[JSompis]

$\frac{1}{2\times{5}} = \frac{1}{3}(\frac{1}{2} - \frac{1}{5})$

$\frac{1}{5\times{8}} = \frac{1}{3}(\frac{1}{5} - \frac{1}{8})$

...

...

$\frac{1}{20\times{23}} = \frac{1}{3}(\frac{1}{20} - \frac{1}{23})$


$\therefore \frac{1}{2\times{5}} + \frac{1}{5\times{8}} + ... + \frac{1}{20\times{23}}$

$= \frac{1}{3}(\frac{1}{2} - \frac{1}{5}) + \frac{1}{3}(\frac{1}{5} - \frac{1}{8}) + ... + \frac{1}{3}(\frac{1}{20} - \frac{1}{23})$

$= \frac{1}{3}(\frac{1}{2} - \frac{1}{23})$

$= \frac{7}{46}$