1/(1×2×3)+1/(2×3×4)+1/(3×4×5)+. ..+1/(18×19×20)=(1/2)(1/1*2-1/2*3)+(1/2)(1/2*3-1/3*4)+......+(1/2)(1/18*19-1/19*20)=(1/2)[1/(1*2)-1/(2*3)+1/(2*3)-1/(3*4)+......-1/(19*20)]=(1/2)*[1/(1*2)-1/(19*20)]=(1/2)*(189/380)=189/760
0.248684