Question

恒等变换1/1*2 +1/2*3 + 1/3*4 +1/4*5 +1/5*6 +1/6*7 +1/7*8 + 1/8*9

Answer 1

1/n(n+1)=1/n-1/(n+1)

1/1*2 +1/2*3 + 1/3*4 +1/4*5 +1/5*6 +1/6*7 +1/7*8 + 1/8*9 + 1/9*10

=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+(1/9-1/10)

=1-1/10

=9/10