题目内容
已知等比数列{an}的各项均为正数,且a1+2a2=1,a
=4a2a6.
(1)求数列{an}的通项公式;
(2)设bn=log2a1+log2a2+…+log2an,求数列{
}的前n项和.
23 |
(1)求数列{an}的通项公式;
(2)设bn=log2a1+log2a2+…+log2an,求数列{
1 |
bn |
(1)设等比数列{an}的公比为q,由a
=4a2a6得a
=4
,
∴q2=
,由已知an>0,∴q=
,
由a1+2a2=1,得2a1=1,∴a1=
,
∴数列{an}的通项公式为an=
.
(2)bn=log2a1+log2a2+…+log2an=-(1+2+…+n)=-
∴
=-
=-2(
-
),
∴数列{
}的前n项和=-2[(1-
)+(
-
)+…+(
-
)]=-
.
23 |
23 |
a | 24 |
∴q2=
1 |
4 |
1 |
2 |
由a1+2a2=1,得2a1=1,∴a1=
1 |
2 |
∴数列{an}的通项公式为an=
1 |
2n |
(2)bn=log2a1+log2a2+…+log2an=-(1+2+…+n)=-
n(n+1) |
2 |
∴
1 |
bn |
2 |
n(n+1) |
1 |
n |
1 |
n+1 |
∴数列{
1 |
bn |
1 |
2 |
1 |
2 |
1 |
3 |
1 |
n |
1 |
n+1 |
2n |
n+1 |
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