1/1*2+1/2*3..+1/19*20
=1-1/2+1/2-1/3+1/3-1/4+……+1/19-1/20
=1-1/20
=19/201-1/2+1/2-1/3+1/3-1/4+……+1/19-1/20=1-1/20为什么1/1*2+1/2*3.。。。。。+1/18*19+1/19*20 =1-1/2+1/2-1/3+1/3-1/4+……+1/18-1/19+1/19-1/20=1-1/20=19/20