La stilul acesta de exercitii se foloseste relatia[tex] \frac{1}{n(n+1)} = \frac{1}{n} - \frac{1}{n+1} [/tex]
Suma care trebuie calculata va deveni
[tex] \frac{1}{5}- \frac{1}{6}+ \frac{1}{6}- \frac{1}{7}+ \frac{1}{7}- \frac{1}{8}+... +\frac{1}{15}- \frac{1}{16}+ \frac{1}{16}- \frac{1}{17} [/tex]
Dupa reducere se obtine [tex] \frac{1}{5}- \frac{1}{17} = \frac{12}{85} [/tex]
