数列的算术平均和几何平均极限问题的探讨

摘要

证明了数列算术平均极限和几何平均极限的两个命题，讨论了数列算术平均极限和几何平均极限与原数列极限的关系，并通过例题分析和求解，给出了数列算术平均和几何平均极限的应用，为求解数列极限提供了简便方法和思路。%The two propositions on the limit of the arithmetic and geometric mean sequence are proved. The relation of the limits of a sequence and its arithmetic and geometric mean sequence is discussed. In order to provide a simple method to solve the sequence limit problems,applications to analysis and solution of some examples are illustrated.