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等差数列{an}，{bn}的前n项和分别为Sn，Tn，若SnTn=2n3n+1，则anbn=（）A.23B.2n−13n−1C.2n+13n+1D.2n−13n+4
题目内容：
等差数列{an}，{bn}的前n项和分别为Sn，Tn，若Sn Tn
=2n 3n+1
，则an bn
=（ ）
A. 2 3
B. 2n−1 3n−1
C. 2n+1 3n+1
D. 2n−1 3n+4
优质解答
∵an bn
＝2an 2bn
＝a1+a2n−1 b1+b2n−1
=(2n−1)(a1+a2n−1) 2
(2n−1)(b1+b2n−1) 2
＝s2n−1 T2n−1
∴an bn
=2(2n−1) 3(2n−1)+1
=2n−1 3n−1
故选B．
| Sn |
| Tn |
| 2n |
| 3n+1 |
| an |
| bn |
A.
| 2 |
| 3 |
B.
| 2n−1 |
| 3n−1 |
C.
| 2n+1 |
| 3n+1 |
D.
| 2n−1 |
| 3n+4 |
优质解答
| an |
| bn |
| 2an |
| 2bn |
| a1+a2n−1 |
| b1+b2n−1 |
| ||
|
| s2n−1 |
| T2n−1 |
∴
| an |
| bn |
| 2(2n−1) |
| 3(2n−1)+1 |
| 2n−1 |
| 3n−1 |
故选B．
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