1/1*2*3=(1/1*2-1/2*3)÷2
1/2*3*4=(1/2*3-1/3*4)÷2
1/3*4*5=(1/3*4-1/4*5)÷2
.
1/18*19*21=(1/18*19-1/19*20)÷2
1/1*2*3+1/2*3*4+1/3*4*5+.1/18*19*20
=(1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+.+1/17*18-1/18*19+1/18*19-1/19*20)÷
2
=(1/1*2-1/19*20)÷2
=(1/2-1/380)÷2
=(189/380)÷2
=189/760