题目内容
已知A=
，B=
+
+
+…+
，请比较A和B的大小．
| 1 |
| 8 |
| 1 |
| 82 |
| 1 |
| 92 |
| 1 |
| 102 |
| 1 |
| 642 |
考点：分数的大小比较
专题：运算顺序及法则
分析：利用放缩法，可得B=
+
+
+…+
＜
+
+
+…+
=
+
-
+
-
+…+
-
=
+
-
=
=A，据此判断出A和B的大小即可．
| 1 |
| 82 |
| 1 |
| 92 |
| 1 |
| 102 |
| 1 |
| 642 |
| 1 |
| 82 |
| 1 |
| 8×9 |
| 1 |
| 9×10 |
| 1 |
| 63×64 |
| 1 |
| 64 |
| 1 |
| 8 |
| 1 |
| 9 |
| 1 |
| 9 |
| 1 |
| 10 |
| 1 |
| 63 |
| 1 |
| 64 |
| 1 |
| 64 |
| 1 |
| 8 |
| 1 |
| 64 |
| 1 |
| 8 |
解答：
解：B=
+
+
+…+
＜
+
+
+…+
=
+
-
+
-
+…+
-
=
+
-
=
=A
所以A＞B．
| 1 |
| 82 |
| 1 |
| 92 |
| 1 |
| 102 |
| 1 |
| 642 |
＜
| 1 |
| 82 |
| 1 |
| 8×9 |
| 1 |
| 9×10 |
| 1 |
| 63×64 |
=
| 1 |
| 64 |
| 1 |
| 8 |
| 1 |
| 9 |
| 1 |
| 9 |
| 1 |
| 10 |
| 1 |
| 63 |
| 1 |
| 64 |
=
| 1 |
| 64 |
| 1 |
| 8 |
| 1 |
| 64 |
=
| 1 |
| 8 |
所以A＞B．
点评：此题主要考查了分数大小的比较，解答此题的关键是放缩法的灵活应用．
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