是1/(1*2)+1/(2*3)+1/(3*4)+.+1/(9*10)吧
1/(1*2)+1/(2*3)+1/(3*4)+.+1/(9*10)
=(1/1-1/2)+(1/2-1/3)+……+(1/9-1/10)
=1-1/2+1/2-1/3+……+1/9-1/10
=1-1/10
=9/10