题目内容

1
2•4
+
1
3•5
+
1
4•6
+…+
1
(n+1)(n+3)
=______.
数列的通项an=
1
(n+1)(n+3)
=
1
2
1
n+1
-
1
n+3
),
1
2•4
+
1
3•5
+
1
4•6
+…+
1
(n+1)(n+3)
=
1
2
1
2
-
1
4
+
1
3
-
1
5
+
1
4
-
1
6
+…+
1
n-1
-
1
n+1
+
1
n
-
1
n+2
+
1
n+1
-
1
n+3

=
1
2
(
1
2
+
1
3
-
1
n+2
-
1
n+3
)

故答案为:
1
2
(
1
2
+
1
3
-
1
n+2
-
1
n+3
)
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