公式S_0=(a_1-a_nq)/(1-q)教材上使用的是“错位相减法”。这种方法用途很广,比如说在求一个等比数列{a_n}与一个等差数列{b_n}对应项积的数列{a_n·b_n}的前n项和时,就可以如此求得: 设{a_n}的公比为q,{b_n}的的公差为d: S_n=a_1b_1+a_2b_+…+a_nb_n (1) 在(1)两边同时乘以{a_n}的公比q: qS_n=a_1b_1q+a_2b_2q+…+a_nb_nq The formula S_0=(a_1-a_nq)/(1-q) uses the “subtraction-subtracting method”. This method is very versatile. For example, when the sum of the first n terms of a {a_n·b_n} sequence of {a_n} equal number series {a_n} and an {α_n} corresponding to an arithmetic sequence {b_n} is obtained, it can be obtained as follows: The common ratio of {a_n} is q, and the tolerance of {b_n} is d: S_n=a_1b_1+a_2b_+...+a_nb_n (1) On both sides of (1), the common ratio of {a_n} is multiplied by q: qS_n=a_1b_1q+ A_2b_2q+...+a_nb_nq