11×4+14×7+17×10+…+1(3n−2)(3n+1)=(  ) A.n3n+1 B.n+13n+1 C.2n−13n+1 D.2n−23n+1

问题描述:

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

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.