1*2分之1+2*3分之1+3*4分之1+4*5分之1+····+9*10分之1
=1/（1*2）+1/(2*3)+1/(3*4)+1/(4*5)+.+1/(9*10)
=(1-1/2)+(1/2-1/3)+.+(1/9-1/10)
=1-1/10
=9/10