[tex]\displaystyle \frac{1}{4 \times 5} + \frac{1}{5 \times 6} +...+ \frac{1}{59 \times 60} = \frac{1}{4} - \frac{1}{5} + \frac{1}{5} +...+ \frac{1}{59} - \frac{1}{60} = \\ \\ = \frac{1}{4} - \frac{1}{60} = \frac{15-1}{60} = \frac{14}{60} = \frac{7}{30} [/tex]
