[tex]A=\frac{1}{1*2} +\frac{1}{2*3} +...... + \frac{1}{9*10}[/tex]
Folosim forma generala : [tex]\frac{1}{a(+1)} = \frac{1}{a} - \frac{1}{a+1}[/tex]
[tex]A= 1- \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + \frac{1}{9} - \frac{1}{10}[/tex]
[tex]A=1-\frac{1}{10} => A=\frac{(10-1)}{10} = \frac{9}{10} \\A=0,9[/tex]
[tex]B=\frac{2}{1*3} + \frac{2}{3*5} + \frac{2}{9*11}[/tex]
[tex]B=\frac{1}{1} - \frac{1}{11}[/tex]
[tex]B=\frac{(11-1)}{11} = > B=\frac{10}{11}[/tex]
