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ข้อ 14. จัดรูปได้

$\displaystyle \sum_{k = 1}^{360}\frac{1}{\sqrt{k(k+1)}(\sqrt{k}+\sqrt{k+1})} $

$=\displaystyle\sum_{k=1}^{360}\frac{\sqrt{k+1}-\sqrt{k}}{\sqrt{k(k+1)}}$

$=\displaystyle\sum_{k=1}^{360}(\frac{1}{\sqrt{k}} - \frac{1}{\sqrt{k+1}})$

$=\displaystyle 1-\frac{1}{19} = \frac{18}{19} = \frac{m}{n}$

$\therefore\,\, m+n=37$