n/(n+1)!=[(n+1)-1]/(n+1)!=(n+1)/(n+1)!-1/(n+1)!=1/n!-1/(n+1)!所以原式=1/1!-1/2!+1/2!-1/3!+……+1/n!-1/(n+1)!=1-1/(n+1)!
1 - 1/(1 + n)!
