跪求:当x趋近于无穷大时,求1/﹙n×n+n+1﹚+2/﹙n×n+n+2﹚+…+n/﹙n×n+n+n﹚的极限
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/07/18 19:43:13
跪求:当x趋近于无穷大时,求1/﹙n×n+n+1﹚+2/﹙n×n+n+2﹚+…+n/﹙n×n+n+n﹚的极限
用夹逼定理
设S=1/﹙n×n+n+1﹚+2/﹙n×n+n+2﹚+…+n/﹙n×n+n+n﹚
1/﹙n×n+n+n﹚+2/﹙n×n+n+2﹚+…+n/﹙n×n+n+n﹚≤S≤1/﹙n×n+n+1﹚+2/﹙n×n+n+1﹚+…+n/﹙n×n+n+1﹚
(1+2+...+n)/﹙n×n+n+n﹚≤S≤(1+2+...+n)/﹙n×n+n+1﹚
1/2*n(n+1)/﹙n×n+n+n﹚≤S≤1/2*n(n+1)/﹙n×n+n+1﹚
用夹逼定理得极限1/2
设S=1/﹙n×n+n+1﹚+2/﹙n×n+n+2﹚+…+n/﹙n×n+n+n﹚
1/﹙n×n+n+n﹚+2/﹙n×n+n+2﹚+…+n/﹙n×n+n+n﹚≤S≤1/﹙n×n+n+1﹚+2/﹙n×n+n+1﹚+…+n/﹙n×n+n+1﹚
(1+2+...+n)/﹙n×n+n+n﹚≤S≤(1+2+...+n)/﹙n×n+n+1﹚
1/2*n(n+1)/﹙n×n+n+n﹚≤S≤1/2*n(n+1)/﹙n×n+n+1﹚
用夹逼定理得极限1/2
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