1、
根據(jù)題意,得
Sn=2^(n+2)-4=4(2^n-1)
a1=S1=4(2^1-1)=4
an=Sn-Sn-1=4(2^n-1)-4[2^(n-1)]=4[2^n-2^(n-1)]=2(2*2^n-2^n)=2^(n+1)
n=1時(shí),同樣成立.
{an}的通項(xiàng)公式為an=2^(n+1)
2.
bn=anlog2(an)
=2^(n+1)log2[2^(n+1)]
=(n+1)2^(n+1)
Tn=b1+b2+...+bn=2*2^2+3*2^3+...+n2^n+(n+1)2^(n+1)
Tn/2=2*2+3*2^2+4*2^3+...+(n+1)2^n
Tn/2-Tn=2*2+2^2+2^3+...+2^n-(n+1)2^(n+1)
=2+2+2^2+2^3+...+2^n-(n+1)2^(n+1)
=2+2(2^n-1)/(2-1)-(n+1)2^(n+1)
=2+2^(n+1)-2-n2^(n+1)-2^(n+1)
=-n2^(n+1)
Tn/2=n2^(n+1)
Tn=n*2^(n+2)