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
答
原式=
(1-1 3
)+1 4
(1 3
-1 4
)+…+1 7
(1 3
-1 3n−2
)=1 3n+1
[(1-1 3
)+(1 4
-1 4
)+…+(1 7
-1 3n−2
)]=1 3n+1
(1-1 3
)=1 3n+1
;n 3n+1
故选A.