已知等比数列{an}各项为实数且公比为q,前前n项和为Sn,S3,S9,S6成等差数列,求证：a2,a8,a5成等差数列
问题描述：
已知等比数列{an}各项为实数且公比为q,前前n项和为Sn,S3,S9,S6成等差数列,求证：a2,a8,a5成等差数列
答
a(n) = aq^(n-1),
a = a(1) = S(1) 0,
q = 1时,S(n) = na 0.满足要求.
q不等于1时,
S(n) = a[q^n-1]/(q-1).
q1时,q^n-10,q-10,S(n) = a[q^n-1]/(q-1) 0.满足要求.
-1q1时,q^n - 1 0,q - 1 0,满足要求.
q = -1时,S(2m) = a[(-1)^(2m) - 1]/(-1-1) = 0,不满足要求.
q -1时,S(2m) = a[q^(2m) - 1]/(q-1) = a[(q^2)^m - 1]/(q-1),
(q^2)^m - 1 0,q - 1 0,S(2m) 0,不满足要求.
因此,
q的取值范围为q-1.