题目内容
观察式子
=
(1-
)，
=
(
-
)，
=
(
-
)，…由此可知
+
+
+…+
=______．
| 1 |
| 1×3 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 3×5 |
| 1 |
| 3 |
| 1 |
| 3 |
| 1 |
| 5 |
| 1 |
| 5×7 |
| 1 |
| 2 |
| 1 |
| 5 |
| 1 |
| 7 |
| 1 |
| 1×3 |
| 1 |
| 3×5 |
| 1 |
| 5×7 |
| 1 |
| (2n-1)×(2n+1) |
原式=
（1-
）+
（
-
）+…+
（
-
）
=
（1-
+
-
+…+
-
）
=
（1-
）
=
×
=
．
故答案为
．
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 5 |
| 1 |
| 2 |
| 1 |
| 2n-1 |
| 1 |
| 2n+1 |
=
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 3 |
| 1 |
| 5 |
| 1 |
| 2n-1 |
| 1 |
| 2n+1 |
=
| 1 |
| 2 |
| 1 |
| 2n+1 |
=
| 1 |
| 2 |
| 2n |
| 2n+1 |
=
| n |
| 2n+1 |
故答案为
| n |
| 2n+1 |
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