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LB^8zX1O0yhoLojE diff --git a/advanced-math/exercise/8-infinite-series/infinite-series.tex b/advanced-math/exercise/8-infinite-series/infinite-series.tex index 859817a..ea9b9e9 100644 --- a/advanced-math/exercise/8-infinite-series/infinite-series.tex +++ b/advanced-math/exercise/8-infinite-series/infinite-series.tex @@ -38,6 +38,8 @@ \subsection{正项级数} +如果题目中没有说明,要首先证明多项式为正数,否则不能使用正项级数的方法。 + \subsubsection{放缩法} 即根据收敛准则来进行判断。如果要判断原级数收敛,则辅助级数应该是对其放大,判断原级数发散,则辅助级数应该是对其缩小。 @@ -56,6 +58,8 @@ $p$级数:$\sum\limits_{n=1}^\infty\dfrac{1}{n^p}\left\{\begin{array}{l} \vert q\vert\geqslant 1, \text{发散} \end{array}\right.$。 +当不知道用哪个时可以使用洛必达先计算一下极限值。 + \subsubsection{比值判别法} 适用于含有$a^n$,$n!$,$n^n$的通项。主要是$n!$。 diff --git a/advanced-math/exercise/9-differential-equation/differential-equation.pdf b/advanced-math/exercise/9-differential-equation/differential-equation.pdf index 8163f5dd449ac2e1aa6fd6d2438692bb60c75ef2..a2f11261cfaf2153b3dd14bff042a5a84f75570b 100644 GIT binary patch delta 84024 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