1除以(1乘以2乘以3)加上1除以(2乘以4乘以3)加上1除以(3乘以4乘以5)加上.1除以(8乘以9乘以10)

1/1*2*3+1/2*3*4+……1/8*9*10
=1/2(1/1*2-1/2*3)+1/2(1/2*3-1/3*4)+...+1/2[1/8*9-1/9*10]
=1/2[1/1*2-1/2*3+1/2*3-1/3*4+...+1/8*9-1/9*10]
=1/2[1/1*2-1/9*10]
=1/2*[1/2-1/90]
=11/45