题目内容
计算| 1 |
| 22-1 |
| 1 |
| 32-1 |
| 1 |
| 42-1 |
| 1 |
| 52-1 |
| 1 |
| 192-1 |
| 1 |
| 202-1 |
分析：由于题目利用平方差公式可以变为
+
+
+
+…+
+
，然后可以变为
(1-
+
-
+
-
+
-
+…+
-
+
-
)，然后计算括号内面的即可求解．
| 1 |
| 1×3 |
| 1 |
| 2×4 |
| 1 |
| 3×5 |
| 1 |
| 4×6 |
| 1 |
| 18×20 |
| 1 |
| 19×21 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 2 |
| 1 |
| 4 |
| 1 |
| 3 |
| 1 |
| 5 |
| 1 |
| 4 |
| 1 |
| 6 |
| 1 |
| 18 |
| 1 |
| 20 |
| 1 |
| 19 |
| 1 |
| 21 |
解答：解：原式=
+
+
+
+…+
+
=
(1-
+
-
+
-
+
-
+…+
-
+
-
)
=
(1+
-
-
)
=
．
| 1 |
| 1×3 |
| 1 |
| 2×4 |
| 1 |
| 3×5 |
| 1 |
| 4×6 |
| 1 |
| 18×20 |
| 1 |
| 19×21 |
=
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 2 |
| 1 |
| 4 |
| 1 |
| 3 |
| 1 |
| 5 |
| 1 |
| 4 |
| 1 |
| 6 |
| 1 |
| 18 |
| 1 |
| 20 |
| 1 |
| 19 |
| 1 |
| 21 |
=
| 1 |
| 2 |
| 1 |
| 2 |
| 1 |
| 20 |
| 1 |
| 21 |
=
| 589 |
| 840 |
点评：此题主要考查了有理数的混合运算，解题的关键是首先利用平方差公式把题目变形，然后利用规律解决问题．
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