> 数学 >
lim
n→∞
[n(1-
1
3
)(1-
1
4
)(1-
1
5
)…(1-
1
n+2
)]等于(  )
A. 0
B. 1
C. 2
D. 3
人气:242 ℃ 时间:2020-04-11 14:35:03
解答
lim
n→∞
[n(1-
1
3
)(1-
1
4
)(1-
1
5
)(1-
1
n+2
)]
=
lim
n→∞
[n×
2
3
×
3
4
×
4
5
×…×
n+1
n+2
]
=
lim
n→∞
2n
n+2

=2.
故选C.
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