Question

计算 2/（1*2*3）+2/（2*3*4）+2/（3*4*5)+...+2/(18*19*20)=

Answer 1

2/(1*2*3)+2/(2*3*4)+2/(3*4*5).+2/(18*19*20)

=(1/1*2-1/2*3)+(1/2*3-1/3*4)+(1/3*4-1/4*5)+...+(1/18*19-1/19*20)

=1/1*2-1/2*3+1/2*3-1/3*4+1/3*4-1/4*5+...+1/18*19-1/19*20

=1/1*2-1/19*20

=1/2-1/380

=189/380