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

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

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

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

(1)k/(k+1)!=[(k+1)-1]/(k+1)!=(k+1)/(k+1)! - 1/(k+1)!=1/k!-1/(k+1)!
(2)运用(1)的结论,累加即可