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在与数列有关的等式中,将数列项下标中的n升为n+k或降为n-k(k∈*N),所得的新等式与原等式对应相减,为解题创造条件的方法,称为变标相减法.此法是解数列题的一种技巧,当用常规方法不易奏效时,可以尝试用变标相减法为解题开辟新的途径.例1数列{an}的前n项和为Sn,若对所有正整数n都有an≠0,且Sn+Sn+1=kan+1,问:是否存在正整数k,使得数列{an}成等比数列?若存在,求出k的值;若不存在,请说明理由.
In series-dependent equations, n in a subscript of a sequence item is raised to n + k or reduced to nk (k∈ * N), and the resulting new equation is subtracted from the original equation to create a solution to the problem Condition method, called the variable subtraction method.This method is to solve the problem of a series of skills, when the conventional method is not easy to work, you can try to use variable-scale subtraction method to open up new ways to solve problems.Examples 1 {an { } Is the first n terms and is Sn, if all positive integers n have an ≠ 0, and Sn + Sn + 1 = kan + 1, Q: Is there a positive integer k, making the sequence {an} into an equal sequence? If there is, find the value of k; if not, please explain the reasons.