> 数学 >
lim
n→∞
[
1
1•4
+
1
4•7
+
1
7•10
+…+
1
(3n−2)(3n+1)
]
=______.
人气:228 ℃ 时间:2020-05-11 09:35:43
解答
lim
n→∞
[
1
1•4
+
1
4•7
+
1
7•10
+…+
1
(3n−2)(3n+1)
]

=
lim
n→∞
1
3
[(1−
1
4
)+(
1
4
1
7
)+…+(
1
3n−2
1
3n+1
)

=
lim
n→∞
1
3
(1−
1
3n+1
)

=
lim
n→∞
1
3
3n
3n+1
=
1
3

故答案为
1
3
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