急``````求教``高中数学````极限题用数学归纳法证明:1×1!+2×2!+3×3!+`````+n×n!=(n+1)!-1(n∈N*)证明:假设当n=k(k∈N*)时等式成立,即1×1!+2×2!+3×3!+`````+k×k!=(k+1)!-1,当n=k+1时,有1×1!+2×2!+3×3!+`````+k×k!+(
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 01:29:25
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急``````求教``高中数学````极限题用数学归纳法证明:1×1!+2×2!+3×3!+`````+n×n!=(n+1)!-1(n∈N*)证明:假设当n=k(k∈N*)时等式成立,即1×1!+2×2!+3×3!+`````+k×k!=(k+1)!-1,当n=k+1时,有1×1!+2×2!+3×3!+`````+k×k!+(
急``````求教``高中数学````极限题
用数学归纳法证明:1×1!+2×2!+3×3!+`````+n×n!=(n+1)!-1(n∈N*)
证明:假设当n=k(k∈N*)时等式成立,即
1×1!+2×2!+3×3!+`````+k×k!=(k+1)!-1,
当n=k+1时,有
1×1!+2×2!+3×3!+`````+k×k!+(k+1)(k+1)!
=(k+1)!-1+(k+1)(k+1)!
=(k+1)![1+(k+1)]-1
=(k+2)(k+1)!-1
=(k+2)!-1
所以n=k+1时等式成立.
(k+2)(k+1)!-1 怎么变成 (k+2)!-1 的
急``````求教``高中数学````极限题用数学归纳法证明:1×1!+2×2!+3×3!+`````+n×n!=(n+1)!-1(n∈N*)证明:假设当n=k(k∈N*)时等式成立,即1×1!+2×2!+3×3!+`````+k×k!=(k+1)!-1,当n=k+1时,有1×1!+2×2!+3×3!+`````+k×k!+(
是这样的
(k+2)!=(k+2)(k+1)k.
(k+1)!=(k+1)k.左右两面都乘以k+2得
(k+2)(k+1)!=(k+2)(k+1)k.=(k+2)!
先弄懂阶乘的定义吧.