数列{an}的首项a1=1,前n项和Sn满足关系:3tSn-(2t+3)Sn-1=3t(t>0,n=2,3,4,5,).
问题描述:
数列{an}的首项a1=1,前n项和Sn满足关系:3tSn-(2t+3)Sn-1=3t(t>0,n=2,3,4,5,).
求和:b1b2-b2b3+b3b4-b4b5+...+(-1)^n+1bnbn+1.
(1)数列{an}是等比数列(要有推理过程);(2)设数列{an}的公比为f(t),做数列{bn},使b1=1,bn=f(1/b(n-1))(n=2,…),求数列{bn}
以上是(3)
答
(1)a1=13tSn- (2t+3) Sn-1=3t (t >0,n=2,3,4,5,) (1).3tSn-1-(2t+3)Sn-2=3t (t >0,n=2,3,4,5,) (2).(1)-(2)得:3tSn- (2t+3) Sn-1= 3tSn-1-(2t+3)Sn-2整理得:3tSn-3tSn-1=(2t+3) Sn-1-(2t+3)Sn-2即...