1*2分之1+2*3分之1+3*4分之1+.+8*9分之1+9*10分之1＝1/(1x2) + 1/(2x3)+1/(3x4)+...+1/(8x9) + 1/(9x10) =(1/1 -1/2) + (1/2 -1/3) + (1/3 -1/4) +...+(1/8-1/9) +(1/9-1/10) =1/1 - 1/10 =9/10