1/1*3=(1-1/3)/2
1/2*4=(1/2-1/4)/2
1/3*5=(1/3-1/5)/2
1/4*6=(1/4-1/6)/2
.
1/18*20=(1/18-1/20)/2
所以
1/1乘3+1/2乘4+1/3乘5+...+1/18乘20.
=(1-1/3)/2+(1/2-1/4)/2+(1/3-1/5)/2+(1/4-1/6)/2+.+(1/18-1/20)/2
=(1-1/3+1/2-1/4+1/3-1/5+1/4-1/6+.+1/18-1/20)/2
=(1+1/2-1/19-1/20)/2
=(531/380)/2
=531/760