问题 填空题
lim
n→∞
[
1
1•4
+
1
4•7
+
1
7•10
+…+
1
(3n-2)(3n+1)
]
=______.
答案

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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