原式
=1/25 [1/(1*2) + 1/(2*3) + ...+ 1/(19*20)]
=1/25 [1/1-1/2 + 1/2 - 1/3 + ...+ 1/19 - 1/20]
=1/25 [1/1 -1/20]
=1/25 [19/20]
=19/500