这道数学求极限要怎么做啊
来源:学生作业帮 编辑:搜搜做题作业网作业帮 分类:数学作业 时间:2024/07/19 06:05:03
这道数学求极限要怎么做啊
![这道数学求极限要怎么做啊](/uploads/image/z/19181380-4-0.jpg?t=%E8%BF%99%E9%81%93%E6%95%B0%E5%AD%A6%E6%B1%82%E6%9E%81%E9%99%90%E8%A6%81%E6%80%8E%E4%B9%88%E5%81%9A%E5%95%8A)
设f(n) = n^n / (n!)^2
则lim f(n+1) / f(n)
= lim (1+1/n)^n / (n+1)
= lim e / (n+1) = 0
所以lim f(n) = 0
则lim f(n+1) / f(n)
= lim (1+1/n)^n / (n+1)
= lim e / (n+1) = 0
所以lim f(n) = 0