问题 选择题
1
1×3
+
1
2×4
+
1
3×5
+
1
4×6
+…+
1
n(n+2)
=(  )
A.
1
n(n+2)
B.
1
2
(1-
1
n+2
C.
1
2
3
2
-
1
n+1
-
1
n+2
D.
1
2
(1-
1
n+1
答案

1
n(n+2)
=
1
2
(
1
n
-
1
n+2
)

1
1×3
+
1
2×4
+
1
3×5
+
1
4×6
+…+
1
n(n+2)

=

1
2
[(1-
1
3
)+(
1
2
-
1
4
)+(
1
3
-
1
5
)+(
1
4
-
1
6
)+…+(
1
n-2
-
1
n
)+(
1
n-1
-
1
n+1
)+(
1
n
-
1
n+2
)]

=

1
2
(1+
1
2
-
1
n+1
-
1
n+2

=

1
2
3
2
-
1
n+1
-
1
n+2
),

故答案选C.

单项选择题
问答题 简答题