a1=4,S3 S2 S4

题目

a1=4,S3 S2 S4
等比数列an中a1=4,前n项和Sn满足S3 S2 S4成等差数列,(1)求an通项公式 (2)设bn=log2丨an丨,Tn为数列{1/bn*bn+1}的前n项和,求Tn?

答案

a1*(1-q^3)/(1-q)+a1*(1-q^4)/(1-q)=2*a1*(1-q^2)/(1-q)
解得：q=0(舍去),q=1,q=-2
q=1时,an=4,
q=-2时,an=4*(-2)^(n-1)
(2)bn=n+1
Tn=1/(2+3)+1/(3+4) +.+1/(n+n+1)
=1/2-1/3+1/3-1/4+.+1/n-1/n+1
=1/2-1/n+1