求((n+1)/(n+2))^3n的极限,麻烦给出重要的步骤.
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/18 12:23:18
![求((n+1)/(n+2))^3n的极限,麻烦给出重要的步骤.](/uploads/image/z/9733162-58-2.jpg?t=%E6%B1%82%28%28n%2B1%29%2F%28n%2B2%29%29%5E3n%E7%9A%84%E6%9E%81%E9%99%90%2C%E9%BA%BB%E7%83%A6%E7%BB%99%E5%87%BA%E9%87%8D%E8%A6%81%E7%9A%84%E6%AD%A5%E9%AA%A4.)
xPMK@+sܨe&$ACлP+TޤQP(kɚ~K/2fޛ7z?cEͿE]IN,`I9\okl'jmj&e-I!wxfA7M?Hf 2꤄4S$ߣ$\6bfBiJf$Ar[ &8 XKAXT7eQWc5zhi;+5
+A8]16Yrڇ
求((n+1)/(n+2))^3n的极限,麻烦给出重要的步骤.
求((n+1)/(n+2))^3n的极限,麻烦给出重要的步骤.
求((n+1)/(n+2))^3n的极限,麻烦给出重要的步骤.
((n+1)/(n+2))^3n=(1-1/(n+2))^(-(n+2)*3n/(-n-2))
lim((n+1)/(n+2))^3n=lim(1-1/(n+2))^(-(n+2)*3n/(-n-2))=e^[lim(3n/(-n-2))]=e^(-3).[n->∞]
(n+1)/(n+2) = 1 - 1/(n+2)
ln[((n+1)/(n+2))^3n] = 3n ln(1- 1/(n+2)) = ln(1- 1/(n+2)) / (1/n)
lim[ 3ln(1- 1/(n+2)) / (1/n) 等价无穷小代换 ln(1- 1/(n+2)) ~ 1/(n+2)
= lim[ -3/(n+2) / (1/n)] = lim[ -3n/(n+2)] = -3
原式 = e^(-3)