数列的几乎单调性和交错级数的重排 Series of Almost Monotonicity and Alternating Series Rearrangement

交错级数是数学分析的重点和难点，主要内容包括交错级数的收敛定理和证明过程。本文主要讨论交错级数的重排和数列之间的关系，通过给出数列的几乎单调性的定义来探究一个已收敛的交错级数在何种条件下重排之后依然收敛，并且给出相关证明。 Alternating series is a focal and difficult point in the mathematical analysis. It mainly includes the convergence theorems and the certification process. This paper focuses on discussing the relationships between the rearrangement and the alternating series. Through the definition of almost monotonicity of series, the study explores in what conditions that a convergent alternating series still be convergent when it is rear- ranged, and gives relevant proof.