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

更新时间2019-02-08 20:28:00

很急，求解，谢谢！

~

1/(1*2)+2/(1*2*3)+...+8/(1*2*3*4*5*6*7*8*9)

=(2-1)/(1*2)+(3-1)/(1*2*3)+...+(9-1)/(1*2*3*4*5*6*7*8*9)

=2/(1*2)-1/(1*2)+3/(1*2*3)-1/(1*2*3)+……+9/(1*2*3*4*5*6*7*8*9)-1/(1*2*3*4*5*6*7*8*9)

=1-1/(1*2)+1/(1*2)-1/(1*2*3)+1/(1*2*3)-1/(1*2*3*4)+……+1/(1*2*3*4*5*6*7*8)-1/(1*2*3*4*5*6*7*8*9)

=1-1/(1*2*3*4*5*6*7*8*9)

=1-1/362880

=362879/362880