n→∞ lim(1^n+2^n+...+100^n)^(1/n)
1个回答
展开全部
(1^n+2^n+...+100^n)^(1/n)
=100[(1/100)^n+(2/100)^n+...+1^n)]^(1/n)
而
1=<[(1/100)^n+(2/100)^n+...+1^n)]^(1/n)
<(1+1+...+1)^(1/n)=n^(1/n)→1 (n→∞ )
所以n→∞ lim[(1/100)^n+(2/100)^n+...+1^n)]^(1/n)=1
故n→∞ lim(1^n+2^n+...+100^n)^(1/n)
n→∞ lim100[(1/100)^n+(2/100)^n+...+1^n)]^(1/n)
=100
=100[(1/100)^n+(2/100)^n+...+1^n)]^(1/n)
而
1=<[(1/100)^n+(2/100)^n+...+1^n)]^(1/n)
<(1+1+...+1)^(1/n)=n^(1/n)→1 (n→∞ )
所以n→∞ lim[(1/100)^n+(2/100)^n+...+1^n)]^(1/n)=1
故n→∞ lim(1^n+2^n+...+100^n)^(1/n)
n→∞ lim100[(1/100)^n+(2/100)^n+...+1^n)]^(1/n)
=100
更多追问追答
追问
(1^n+2^n+...+100^n)^(1/n)
=100[(1/100)^n+(2/100)^n+...+1^n)]^(1/n)
应为
(1^n+2^n+...+100^n)^(1/n)
=100^(1/n)[(1/100)^n+(2/100)^n+...+1^n)]^(1/n)
追答
(1^n+2^n+...+100^n)^(1/n)
=[100^n【(1/100)^n+(2/100)^n+...+1^n)】]^(1/n)
=100[(1/100)^n+(2/100)^n+...+1^n)]^(1/n)
本回答被提问者采纳
已赞过
已踩过<
评论
收起
你对这个回答的评价是？
推荐律师服务：
若未解决您的问题，请您详细描述您的问题，通过百度律临进行免费专业咨询
