\u9898\u76ee\u4e3a\uff1a<\/p>\n\n\n\n
$$
\\lim _{n \\rightarrow \\infty} \\frac{\\sqrt[n]{n}}{n}=\\frac{1}{e}
$$<\/p>\n\n\n\n
\u89e3\u7b54\uff1a<\/p>\n\n\n\n
$$
\\begin{array}{c}
\\ln \\left(\\frac{\\sqrt[n]{n !}}{n}\\right)=\\frac{1}{n}(\\ln 1+\\ln 2+\\cdots+\\ln n)-\\ln n \\
=\\frac{1}{n}\\left(\\ln \\left(\\frac{1}{n}\\right)+\\ln \\left(\\frac{2}{n}\\right)+\\cdots+\\ln \\left(\\frac{n}{n}\\right)\\right) \\longrightarrow \\int_{0}^{1} \\ln x d x=-1
\\end{array}
$$<\/p>\n","protected":false},"excerpt":{"rendered":"