Question

数列{an}是以a1=4为首项的等比数列,且S3,S2,S4成等差数列

Answer 1

1.

2S2=S3+S4

2S2=S2+A3+S2+A3+A4

2A3+A4=0

A4/A3=-2

An=A1×q^n=4×(-2)^(n-1)=(-2)^(n+1)

2.

|An|=|(-2)^(n+1)|=2^(n+1)

Bn=log2|An|=log2(2^(n+1)=n+1

1/(Bn×B(n+1)=1/((n+1)×(n+1+1))=((n+2)-(n+1))/((n+1)(n+2))=1/(n+1)-1/(n+2)

Tn=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+……+(1/(n+1)-1/(n+2))

=1/2-1/(n+2)

=n/(2(n+2))