Case studies on problem-solving strategies for the sum of the first n terms in sequences in the national college entrance examination
例析高考数列前n项和问题的求解策略

摘要

高中数学中的“数列求前n和问题”是高考中常见的重点题型，难度一般属于中等偏下，主要考查学生的逻辑推理能力和数学运算能力。本文结合历年高考数学真题，详细分析了六种数列求前n和的方法：求和公式的直接应用、错位相减法、裂项相消法、分组求和法、倒序相加法以及通项公式法，为数列部分的教学和备考提供了参考。

Abstract

Calculating the sum of the first n terms of sequences in high school mathematics is a common and key topic in the National College Entrance Examination (Gaokao), typically categorized as moderately challenging. It primarily assesses students' logical reasoning and mathematical operation skills. By analyzing past Gaokao mathematics questions, this paper systematically elaborates on six solution strategies for sequence summation: direct application of the general term formula, the method of subtraction by dislocation (telescoping series), term-splitting and cancellation method, group summation method, reverse-order addition method, and derivation of the general term formula method. The study aims to provide practical references for teaching and exam preparation in sequence learning.