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)!
数学人气:458 ℃时间:2019-10-29 14:44:50
优质解答
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+...
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