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单词 Root test
释义

Root test

中文百科

根值审敛法

根值审敛法是判别正项级数敛散性的一种方法,又叫做柯西判别法

\sum_{n=1}^\infty a_n为正项级数,如果

C = \lim_{n\rightarrow\infty}\sqrt[n]{a_n},
  • 当C<1时级数收敛
  • 当C>1或C=\infty时级数发散
  • 当C=1时级数可能收敛也可能发散。
英语百科

Root test 根值审敛法

Decision diagram for the root test
Entscheidungsbaum für das Wurzelkriterium

In mathematics, the root test is a criterion for the convergence (a convergence test) of an infinite series. It depends on the quantity

where a_n are the terms of the series, and states that the series converges absolutely if this quantity is less than one but diverges if it is greater than one. It is particularly useful in connection with power series.

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更新时间:2025/6/19 1:02:06