Question

Calculati : $\frac{1}{1X2} + \frac{1}{2X3} + \frac{1}{3X4} + ... + \frac{1}{2013X2014}$

Answer 1

1/(1*2)=  1/1 -1/2
1/(2*3)=  1/2 -1/3
1/(3*4)=  1/3 -1/4
.........................................................        se reduc termenii pe diagonala (-1/2 cu1/2; -1/3 cu 1/3)
1/(2013*2014)= 1/2013 -1/2014

S= (1/1 -1/2014)  aducem la acelasi numitor

S=(2014-1)/2014=  2013/2014