Question

已知数列{an}的前n项和为S,且(a-1)Sn=a(an-1)(a＞0,n∈正整数) 求证数列{an}是等比数列,并求

Answer 1

(a-1)Sn-1=a(an-1-1)两式相减得:(a-1)an=a(an-an-1),即an/an-1=a

(a-1)a1=a(a1-1)得 a1 = a ≠0

所以是等比数列