一道等比数列的题目,求助高手!!!设数列{an}的前n项和为Sn
设数列{an}的前n项和为Sn,(且an不等于0),S1,S2,S3·····Sn····成等比数列,试问a2,a3,a4,···,an,·····成等比数列吗?证明结论! 求助真正高手!!!!
{Sn}成等比数列 ==> Sn = a*q^(n-1) An = Sn -S(n-1) =a*(q-1)*q^(n-2) A(n-1) =a*(q-1)*q^(n-3) an不等于0 ==> a不等于0, q不等于1 An/A(n-1) = q ====> a2,a3,a4,...,an,...成等比数列