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

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

(1)예비 지식:n/[(n+1)!]=[(n+1)-1]/[(n+1)!]=[1/n!]-[1/(n+1)!].(2)원 식=1-(1/9!)=(9!-1)/9!.