Question

Найти простое решение:
$frac{1}{1*2} + frac{1}{2*3} + frac{1}{3*4} + frac{1}{4*5} + frac{1}{5*6}+ frac{1}{6*7} + frac{1}{7*8} + frac{1}{8*9} + frac{1}{9*10}$

Answer 1

1/1*2=1-1/2
1/2*3=1/2-1/3
1/3*4=1/3-1/4
1/4*5=1/4-1/5
.....................
1/9*10=1/9-1/10

S=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