题目内容
若n是大于1的自然数,求证
+
+…+
>
-
.
| 1 |
| 22 |
| 1 |
| 32 |
| 1 |
| n2 |
| 1 |
| 2 |
| 1 |
| n+1 |
证明:∵
>
∴
>
-
∴
+
+…+
>
-
+
-
+…+
-
∴
+
+…+
>
-
| 1 |
| n2 |
| 1 |
| n(n+1) |
∴
| 1 |
| n2 |
| 1 |
| n |
| 1 |
| n+1 |
∴
| 1 |
| 22 |
| 1 |
| 32 |
| 1 |
| n2 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| n |
| 1 |
| n+1 |
∴
| 1 |
| 22 |
| 1 |
| 32 |
| 1 |
| n2 |
| 1 |
| 2 |
| 1 |
| n+1 |
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