众所周知,等比数列前n项和有两种表达式,即,不同之处在于q=1与q≠1．其实对于公比q=1与q≠-1, Sn在有些性质方面也有很大差别,这一点在学习时不可忽视．看下列命题:若{an}是等比数列,Sn是前n项和,则Sk,S2k-Sk,S3k-S2k,…,Snk-S(n-1)k,…是等比数列．好多资料都认为它是一个正确的结论,其实只要举反例:公比q=-1,k为偶数时,就是各项均为0的一个数列,显然该命题就不成立了．同样地,命题:数列{an}是等比数列,则a1+a2,a2+a3,a3+a4,…,an+an+1,…是等比数列．这也是一个假命题．公比为-1的等比数列在求Sn时,有时也不必要非得对项数n进行考虑．如:求和Sn= -1+2-3+4-…+(-1)n·n,大多资料上都 As we all know, there are two kinds of expressions for the first n terms of the geometric progression, that is, the difference is that q=1 and q≠1. In fact, for public ratios q=1 and q≠-1, Sn is also very different in some aspects of nature, this can not be ignored in learning. Look at the following propositions: If {an} is a geometric sequence, Sn is the first n sum, then Sk,S2k-Sk,S3k-S2k,...,Snk-S(n-1)k,... are geometric sequences. A lot of data think that it is a correct conclusion. In fact, as long as we give a counterexample: the public ratio q = -1. When k is an even number, it is a series with all 0s. Obviously the proposition is not established. Similarly, the proposition: The sequence {an} is a geometric sequence, then a1+a2,a2+a3,a3+a4,...,an+an+1,... are geometric sequences. This is also a false proposition. An analogy with a common ratio of -1 is required for Sn, and sometimes it is not necessary to consider the number of entries n. Such as: summation Sn = -1 +2-3 +4-... + (-1) n · n, most of the data are