1/1*2+1/2*3+1/3*4+...+1/99*100答案是什么,具体的方法?

Question

1/1*2+1/2*3+1/3*4+...+1/99*100 答案是什么,具体的方法?

Answer 1

1/1*2+1/2*3+1/3*4+...+1/99*100
=(1-1/2)+(1/2-1/3)+(1/3-1/4)+.*(1/99-1/100)
=1-1/100
=99/100