[tex]S= \frac{1}{1*2} + \frac{1}{2*3} + \frac{1}{3*4} +...+ \frac{1}{200*201} \\ \\ S=( \frac{1}{1} - \frac{1}{2}) + ( \frac{1}{2} - \frac{1}{3} ) + ( \frac{1}{3} - \frac{1}{4} ) +...+ ( \frac{1}{200} - \frac{1}{201}) \\ \\ S = \frac{1}{1} - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} +...+ \frac{1}{200} - \frac{1}{201} \\ \\ S = \frac{1}{1} - \frac{1}{201} \\ \\ S= \frac{201-1}{201} \\ \\ S= \frac{200}{201} [/tex]
Am folosit formula [tex] \frac{1}{n(n+k)} = \frac{1}{n} - \frac{1}{n+k} [/tex].
Sper ca te-am ajutat.
