问题 选择题
数列-
1
3×5
2
5×7
,-
3
7×9
4
9×11
,…
的通项为(  )
A.(-1)n+1
1
(2n+1)(2n+3)
B.(-1)n+1
n
(2n+1)(2n+3)
C.(-1)n
1
(2n+1)(2n+3)
D.(-1)n
n
(2n+1)(2n+3)
答案

由题意可知,a1=-

1
3×5
=(-1)1
1
(2×1+1)(2×2+1)

a2=

2
5×7
=(-1)2
2
(2×2+1)(2×3+1)

a3=

3
7×9
=(-1)3
3
(2×3+1)(2×4+1)

an=(-1)n

n
(2n+1)(2n+3)

故选D

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