> 数学 >
若数列{an}的通项公式为an=
1
(n+1)(n+2)
,其前n项和为
7
18
,则n为(  )
A. 5
B. 6
C. 7
D. 8
人气:286 ℃ 时间:2020-02-05 14:26:48
解答
由题意得,an=
1
(n+1)(n+2)
=
1
n+1
-
1
n+2

所以Sn=a1+a2+…+an=(
1
2
-
1
3
)+(
1
3
-
1
4
)+…+(
1
n+1
-
1
n+2

=
1
2
-
1
n+2
=
n
2(n+2)

n
2(n+2)
=
7
18
,解得n=7,
故选:C.
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