Explicație pas cu pas:
[tex]S = \left(\frac{1}{2\cdot 3} + \frac{1}{3\cdot4} + \frac{1}{4\cdot5} + ... + \frac{1}{31\cdot 32} \right) - \frac{15}{32} = \\ = \left(\frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} +\frac{1}{4} - \frac{1}{5} +...+ \frac{1}{31} - \frac{1}{32} \right) - \frac{15}{32} \\ = \left(\frac{1}{2} - \frac{1}{32} \right) - \frac{15}{32} = \frac{32 - 2}{32} = \frac{30 - 15}{32} \\= \frac{15}{32} [/tex]
