Найти простое решение:
[tex] \frac{1}{1*2} + \frac{1}{2*3} + \frac{1}{3*4} + \frac{1}{4*5} + \frac{1}{5*6}+ \frac{1}{6*7} + \frac{1}{7*8} + \frac{1}{8*9} + \frac{1}{9*10} [/tex]

1/1*2=1-1/21/2*3=1/2-1/31/3*4=1/3-1/41/4*5=1/4-1/5.....................1/9*10=1/9-1/10S=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...-1/9+1/9-1/10=1-1/10=9/10