Question

1/(5*6) + 1/(6*7) + 1/(7*8) + ... + 1/(15*16) + 1/(16*17)

Answer 1

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

Answer 2

Am atasat o rezolvare !