1.k/(k+1)!=1/k!-1/(k+1)! 证明：k/(k+1)!=(（k+1)-1)/(k+1)!=1/k!-1/(k+1)! 2.n/(n+1)!=1/n!-1/(n+1)!(n-1)/n!=1/(n-1)!-1/n!.2/3!=1/2!-1/3!1/2!=1/1!-1/2!以上式子相加,消去式子右边相同的项,得1/2!+2/3!+…n/(n+...