> 数学 >
若S=
1
1×3
+
1
3×5
+…+
1
(2n-1)(2n+1)
,则S=______.
人气:473 ℃ 时间:2020-04-06 14:52:08
解答
1
(2n-1)(2n+1)
=
1
2
1
2n-1
-
1
2n+1

∴S=
1
1×3
+
1
3×5
+…+
1
(2n-1)(2n+1)
=
1
2
(1-
1
3
+
1
3
-
1
5
+…+
1
2n-1
-
1
2n+1
)=
1
2
(1-
1
2n+1

∴S=
n
2n+1

故答案为:
n
2n+1
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