Question

Va rog repedee dau coroana (ex in poza)

Answer 1

Suma:
$\frac{1}{1*2} + \frac{1}{2*3} + \frac{1}{3*4} +...+ \frac{1}{2013*2014} =$
Vom desface astfel:
$\frac{1}{1} - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \frac{1}{3} - \frac{1}{4} +...+ \frac{1}{2013} - \frac{1}{2014} =\ \textgreater$
$=\ \textgreater \ 1- \frac{1}{2014}$
$= \frac{2014-1}{2014}$
$= \frac{2013}{2014}$