Question

Să se calculeze:

$\frac{1}{1*2} + \frac{1}{2*3} + \frac{1}{3*4} +...+ \frac{1}{2016*2017}$

Answer 1

1/1*2=1/1-1/2
1/2*3=1/2-1/3
1/3*4=1/3-1/4
....
1/2016*2017=1/2016-1/2017
_________________________
1/1*2+1/2*3+1/3*4+.....+1/2016*2017=
=1/1-1/2+1/2-1/3+1/3-1/4+.......+1/2016-1/2017=
=1/1-1/2017=(2017-1)/2017=2016/2017