题目内容
计算：
+
+
+
+
+
+
+
=
．
| 1 |
| 2 |
| 1 |
| 4 |
| 1 |
| 8 |
| 1 |
| 31 |
| 1 |
| 62 |
| 1 |
| 124 |
| 1 |
| 248 |
| 1 |
| 496 |
| 15 |
| 16 |
| 15 |
| 16 |
分析：每相邻的两个分数拆项后，都有相同的数，故把每个分数拆为分数相减的形式：
=1-
；
=
-
；
=
-
…然后相加．
| 1 |
| 2 |
| 1 |
| 2 |
| 1 |
| 4 |
| 1 |
| 2 |
| 1 |
| 4 |
| 1 |
| 8 |
| 1 |
| 4 |
| 1 |
| 8 |
解答：解：原式=(1-
)+(
-
)+(
-
)+
+(
-
)+(
-
)+(
-
)+(
-
)，
=1-
+
+
-
，
=
+
×(2-
)=
+
×
，
=
+
=
．
故答案为：
．
| 1 |
| 2 |
| 1 |
| 2 |
| 1 |
| 4 |
| 1 |
| 4 |
| 1 |
| 8 |
| 1 |
| 31 |
| 1 |
| 31 |
| 1 |
| 62 |
| 1 |
| 62 |
| 1 |
| 124 |
| 1 |
| 124 |
| 1 |
| 248 |
| 1 |
| 248 |
| 1 |
| 496 |
=1-
| 1 |
| 8 |
| 1 |
| 31 |
| 1 |
| 31 |
| 1 |
| 496 |
=
| 7 |
| 8 |
| 1 |
| 31 |
| 1 |
| 16 |
| 7 |
| 8 |
| 1 |
| 31 |
| 31 |
| 16 |
=
| 7 |
| 8 |
| 1 |
| 16 |
| 15 |
| 16 |
故答案为：
| 15 |
| 16 |
点评：此题考查了学生对分数的拆项的掌握情况，以及简算的能力．
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