4*4/3*5+6*6/5*7+.+18*18/17*19
=（3*5+1）/(3*5)+(5*7+1)/(5*7）+……+(17*19+1)/(17*19)
=1+1/(3*5)+1+1/（5*7）+……+1+1/(17*19)
=8+(1/2)[2/3*5+2/5*7+……+2/17*19]
=8+(1/2)*(1/3-1/5+1/5-1/7+……+1/17-1/19)
=8+(1/2)(1/3-1/19)=8+8/57=464/57