[tex]a = \frac{1}{1*2} + \frac{1}{2*3} + ... + \frac{1}{9*10} \\ \\ Acum~vom~scrie~pe~1~ca~fiind~2-1,3-2,4-3,etc. \\ \\ a = \frac{2-1}{1*2} + \frac{3-2}{2*3} + ... + \frac{10-9}{9*10} \\ \\ a = \frac{2}{1*2} - \frac{1}{1*2} + \frac{3}{2*3} - \frac{2}{2*3} + ... + \frac{10}{9*10} - \frac{9}{9*10} \\ \\ a = \frac{2}{2} - \frac{1}{2} + \frac{1}{2} - \frac{1}{3} + ... + \frac{1}{9} - \frac{1}{10} \\ \\ Se~reduc~acele~numere~si~ramane \\ \\ a = 1 - \frac{1}{10}[/tex]
[tex]a = \frac{10-1}{10} \\ \\ a = \frac{9}{10} \\ \\ Sper~ca~te-am~ajutat![/tex]
