《高等数学》课程中limn→∞n∑i=1a_i型极限求解方法探讨

Research on Solving Method for limn→∞n∑i=1a_i Type Limit

对limn→∞n∑i=1a_i型极限的求解方法进行探讨,提出三种求解方法:利用数列求和方法对n项和进行化简、再利用极限的四则运算法则;利用夹逼准则;利用定积分的定义。并重点对每种方法的注意事项、使用技巧及适用范围进行了分析和说明。

Several common methods for solving the limit of limn→∞n∑i=1aiare researched in this paper, three approaches are discussed. These include first simplifying the sum of the sequence and then using the limit laws, using the Squeeze Theorem and the definition of a definite integral. Furthermore, the notice, techniques and application range for each method are analyzed and illustrated.