Question

数列题，要详细过程，会的帮帮忙，给好评，第二问

Answer 1

设公比为q，等比数列各项均为正，q>0
a3²=9a2a6
a2²q²=9a2²q⁴
q²=1/9 q>0 q=1/3
2a1+3a2=1
2a1+3a1q=1
q=1/3代入，整理，得3a1=1
a1=1/3
an=a1q^(n-1)=(1/3)(1/3)^(n-1)=1/3ⁿ
数列{an}的通项公式为an=1/3ⁿ
an=1/3ⁿ=3^(-n)
bn=log3(a1)+log3(a2)+...+log3(an)
=log3[3^(-1)]+log3[3^(-2)]+...+log3[3^(-n)]
=-1-2-...-n
=-n(n+1)/2
1/bn=-2/[n(n+1)]=-2[1/n -1/(n+1)]
Tn=1/b1+1/b2+...+1/bn
=-2[1/1-1/2+1/2-1/3+...+1/n -1/(n+1)]
=-2[1- 1/(n+1)]
=-2n/(n+1)