已知公比不为1的等比数列an的首项a1=1/2,当n大于等于3时,求|3+log2an|的前n项和tn

Question

已知公比不为1的等比数列an的首项a1=1/2,当n大于等于3时,求|3+log2an|的前n项和tn

Answer 1

设｛an}的公比为q,q≠1,q>0
∵a1=1/2
∴an=1/2*q^(n-1)
设bn=3+log(2)an
那么
bn=3+log(2)[1/2q^(n-1)]
=3+log(2)(1/2)+log(2)q^(n-1)
=3-1+(n-1)log(2)q
=2+(n-1)log(2)q
=nlog(2)q+2-log(2)q
那么{bn}为等差数列,
公差d=log(2)q,b1=2
当q>1时,d=log(2)q>0
bn>0
|3+log2an|=bn
前n项和
Sn=(b1+bn)*n/2
=[2+nlog(2)q+2-log(2)q]n/2
=[4-log(2)q+nlog(2)q]n/2
当0