1*2*3*4分之1+2*3*4*5分之1+…+17*18*19*20分之1（计算题）
1/1*2*3*4+1/2*3*4*5…………+1/17*18*19*20
=1/2(1/1*4-1/2*3+1/2*5-1/3*4+1/3*6-1/4*5……1/17*20-1/18*19)
=1/2(1/1*4+1/2*5+1/3*6……1/17*20-(1/2*3+1/3*4……1/18*19))
=1/2*(1/3*(1-1/4+1/2-1/5+1/3-1/6+1/4-1/7……1/17-1/20)-(1/2-1/3+1/3-1/4……1/18-1/19))
=1/2*(1/3*(1+1/2+1/3-1/18-1/19-1/20)-(1/2-1/19))
=1/2*(1/3*(5/18-1/19-1/20+3/19))
=1/6*(5/18+2/19-1/20)
=1139/(6*19*180)
=1139/20520