等比数列{an}同时满足下列三个条件：①a1+a6=33；②a3×a4=32；③三个数4a2,2a3,a4 依次成等差数列

1 a1+a1*q^5=33
a1*q^2*a1*q^3=a1^2*q^5=32
4a2+a4=4a3 得：4a1*q+a1*q^3=4*a1*q^2
q^2-4q+4=0 q=2
由a1+a1*q^5=33
得a1=1
所以an=2^(n-1)
2 b(n)=n/a(n)=n/2^(n-1).
T(n)=1/2^(1-1) + 2/2^(2-1) + 3/2^(3-1) + ...+ (n-1)/2^(n-2) + n/2^(n-1)
2T(n) = 1/2^(-1) + 2/2^(1-1) + 3/2^(2-1) +...+(n-1)/2^(n-3) + n/2^(n-2)
T(n)=2T(n)-T(n)=1/2^(-1) + 1/2^(1-1) + 1/2^(2-1) + ...+ 1/2^(n-2) - n/2^(n-1)
= 2 + 1 + 1/2 + ...+ 1/2^(n-2) - n/2^(n-1)
= 2 - n/2^(n-1) + [1-1/2^(n-1)]/(1-1/2)
= 2 - n/2^(n-1) + 2[1 - 1/2^(n-1)]
= 4 - (n+2)/2^(n-1)