摘要：11．2 12．49或7 13． z
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观察下列等式：
×
=1-
×
+
×
=1-
×
+
×
+
×
=1-
…
由以上各式推测第4个等式为
×
+
×
+
×
+
×
=1-
×
+
×
+
×
+
×
=1-
．
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| 3 |
| 1×2 |
| 1 |
| 2 |
| 1 |
| 22 |
| 3 |
| 1×2 |
| 1 |
| 2 |
| 4 |
| 2×3 |
| 1 |
| 22 |
| 1 |
| 3×22 |
| 3 |
| 1×2 |
| 1 |
| 2 |
| 4 |
| 2×3 |
| 1 |
| 22 |
| 5 |
| 3×4 |
| 1 |
| 23 |
| 1 |
| 4×23 |
…
由以上各式推测第4个等式为
| 3 |
| 1×2 |
| 1 |
| 2 |
| 4 |
| 2×3 |
| 1 |
| 22 |
| 5 |
| 3×4 |
| 1 |
| 23 |
| 6 |
| 4×5 |
| 1 |
| 24 |
| 1 |
| 5×24 |
| 3 |
| 1×2 |
| 1 |
| 2 |
| 4 |
| 2×3 |
| 1 |
| 22 |
| 5 |
| 3×4 |
| 1 |
| 23 |
| 6 |
| 4×5 |
| 1 |
| 24 |
| 1 |
| 5×24 |
（2012•黄州区模拟）观察下列等式：
×
=1-
，
×
+
×
=1-
，
×
+
×
+
×
=1-
，…，由以上等式推测到一个一般结论为：
×
+
×
+
×
+…+
×
=1-
（n∈N*）
×
+
×
+
×
+…+
×
=1-
（n∈N*）．
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| 3 |
| 1×2 |
| 1 |
| 2 |
| 1 |
| 22 |
| 3 |
| 1×2 |
| 1 |
| 2 |
| 4 |
| 2×3 |
| 1 |
| 22 |
| 1 |
| 3×22 |
| 3 |
| 1×2 |
| 1 |
| 2 |
| 4 |
| 2×3 |
| 1 |
| 22 |
| 5 |
| 3×4 |
| 1 |
| 23 |
| 1 |
| 4×23 |
| 3 |
| 1×2 |
| 1 |
| 2 |
| 4 |
| 2×3 |
| 1 |
| 22 |
| 5 |
| 3×4 |
| 1 |
| 23 |
| n+2 |
| n(n+1)2n |
| 1 |
| 2n |
| 1 |
| (n+1)2n |
| 3 |
| 1×2 |
| 1 |
| 2 |
| 4 |
| 2×3 |
| 1 |
| 22 |
| 5 |
| 3×4 |
| 1 |
| 23 |
| n+2 |
| n(n+1)2n |
| 1 |
| 2n |
| 1 |
| (n+1)2n |