순서도 부분분수 합

$\displaystyle \frac{1}{\left( 3 n - 1 \right) \left( 3 n + 2 \right)} = \frac{1}{3} \left( \frac{1}{3 n - 1} - \frac{1}{3 n + 2} \right)$이므로 $\displaystyle S = \frac{1}{2 \times 5} + \frac{1}{5 \times 8} + \frac{1}{8 \times 11} + \cdots + \frac{1}{26 \times 29} + \frac{1}{29 \times 32}$ $\displaystyle = \frac{1}{3} \left\{ \left( \frac{1}{2} - \frac{1}{5} \right) + \left( \frac{1}{5} - \frac{1}{8} \right) + \cdots + \left( \frac{1}{29} - \frac{1}{32} \right) \right\}$ $\displaystyle = \frac{1}{3} \left( \frac{1}{2} - \frac{1}{32} \right)$$\displaystyle = \frac{5}{32}$