Instructional Designs for Two Mathematical Contest Questions for College Students

本文对两道中国大学生数学竞赛试题进行了教学设计，给出了适合学生理解运用的方法。对于第一题，我们给出了一个方便处理的幂级数系数的通项公式；对于第二题，我们利用函数的单调性和隐函数的导数以及第二问的结论，给出了第三问的两个新解法。This paper provides instructional designs for two questions from the Chinese Mathematics Competition for College Students, offering methods suitable for students to understand and apply. For the first question, we present a general formula for the coefficients of power series that is convenient to handle. For the second question, we utilize the monotonicity of functions and the derivative of implicit functions, as well as the conclusion of the second part to provide two new methods for the third part.