Question

1/（1*2）＋1/（2*3）＋1/（3*4）＋……＋1／（19＊20）＝用简便算法写出过程

Answer 1

1/1*2+1/2*3+1/3*4+1/4*5+1/5*6.1/19*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