利用高阶泰勒公式解决一类和式极限问题——以一道全国大学生数学竞赛试题为例

Using High-order Taylor’s Formula to Solve a Class of Sum Limit Problem

通过对第十一届全国大学生数学竞赛决赛的一道试题进行联想,讨论了利用泰勒公式对无法直接凑成定积分形式的,如n项和与其极限值之差的等价无穷小的一种做法.

Associations are made through a problem in the 11 th National Mathematics Competition Final for College Students, where finding the equivalent infinitesimal of the difference between the sum of n terms, which cannot be directly formed into a definite integral, and its limit value is given by using Higher-order Taylor’s formula.