按部就班的课堂教学是教师授课的主流,学生的“好问”“善问”常会带来课堂的“意外”收获.在介绍“等差乘等比”数列求和的例题后,有学生“意外”提出通项为a_n=n~2·2~n的数列能否用类似方法求和.抓住这个契机,师生一起通过观察特点、类比方法、分组化归等方法进行探究活动,不但“意外”收获该数列的求和公式,还对它进行了加强以及一般化的推广,最后通过裂项相消法、导数法、组合数公式以及阿贝尔变换数列求和公式等4种不同的方法对结论进行验证. Step-by-step classroom teaching is the mainstream of teacher teaching, students “good question ” “good question ” often bring class “accidental ” in the introduction of Example, students “Accident ” put forward the general term for the a_n = n ~ 2 · 2 ~ n series can use a similar method to seize this opportunity to teachers and students together through observation characteristics, analogy, grouping In addition, the “summertime” method not only harnesses the summation formula of the sequence, but also strengthens it and generalizes it. Finally, through the method of fission cancellation, the derivative method, the combination formula, Bell transformation sequence summation formula and other four different methods to verify the conclusion.