Lim((1²+2²+……+n²)/n³)n→∞=
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 20:06:12
![Lim((1²+2²+……+n²)/n³)n→∞=](/uploads/image/z/7658248-40-8.jpg?t=Lim%EF%BC%88%281%26%23178%3B%EF%BC%8B2%26%23178%3B%EF%BC%8B%E2%80%A6%E2%80%A6%EF%BC%8Bn%26%23178%3B%29%2Fn%26%23179%3B%EF%BC%89n%E2%86%92%E2%88%9E%EF%BC%9D)
Lim((1²+2²+……+n²)/n³)n→∞=
Lim((1²+2²+……+n²)/n³)n→∞=
Lim((1²+2²+……+n²)/n³)n→∞=
1²+2²+……+n²=n(n+1)(2n+1)/6
所以原式=limn(n+1)(2n+1)/6n^3
=lim(1+1/n)(2+1/n)/6
=1*2/6
=1/3
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来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 20:06:12
Lim((1²+2²+……+n²)/n³)n→∞=
Lim((1²+2²+……+n²)/n³)n→∞=
Lim((1²+2²+……+n²)/n³)n→∞=
1²+2²+……+n²=n(n+1)(2n+1)/6
所以原式=limn(n+1)(2n+1)/6n^3
=lim(1+1/n)(2+1/n)/6
=1*2/6
=1/3