问题 选择题
1
1×4
+
1
4×7
+
1
7×10
+…+
1
(3n-2)(3n+1)
=(  )
A.
n
3n+1
B.
n+1
3n+1
C.
2n-1
3n+1
D.
2n-2
3n+1
答案

原式=

1
3
(1-
1
4
)+
1
3
1
4
-
1
7
)+…+
1
3
1
3n-2
-
1
3n+1
)=
1
3
[(1-
1
4
)+(
1
4
-
1
7
)+…+(
1
3n-2
-
1
3n+1
)]=
1
3
(1-
1
3n+1
)=
n
3n+1

故选A.

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