求证：（1）k/(k+1)!=1/k!-1/(k+1)!(2)1/2!+2/3!+…n/(n+1)!=1-1/(n+1)

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+1)!=1/1!-1/(n+1)!=1-1/(n+1)!
是不是很简单
呵呵