新教材第三册(选修Ⅱ)的第二章中引入了一种关于正整数问题的证明方法——数学归纳法,在课本中,数学归纳法主要用来解决几种证明问题:数列求和、整除问题以及几何问题,数列求和是其中的一大类。这里我们介绍用除了数学归纳法之外的方法来证明课本上关于数列求和的问题。一、利用等差、等比数列前n项求和公式在这部分的题目中,有一些是可以直接利用等差或等 The second chapter of the new textbook (elective Ⅱ) introduces a proof of positive integer problem - mathematical induction, in the textbook, mathematical induction is mainly used to solve several proven problems: the sequence of summation , Divisibility problems, and geometry problems, summation of numbers is one of the major categories. Here we introduce methods other than mathematical induction to prove the textbook’s problem of summation of numbers. First, the use of equal-difference, geometric series than the first n summation formula in this part of the title, there are some direct use of equal or equal