题目内容
[x]为x的整数部分．当n≥2时，则[
+
+
+…+
]的值为（ ）
| 1 |
| 12 |
| 1 |
| 22 |
| 1 |
| 32 |
| 1 |
| n2 |
| A．0 | B．1 | C．2 | D．3 |
∵
+
+
+…+
≤1+
+
+…+
=1+（1-
+
-
+…+
-
）
=1+（1-
）=2-
．
+
+
+…+
≥
+
+
+…+
=1-
+
-
+
-
+…+
-
=1-
．
∴当n≥2时，则[
+
+
+…+
]=1．
故选B．
| 1 |
| 12 |
| 1 |
| 22 |
| 1 |
| 32 |
| 1 |
| n2 |
| 1 |
| 1×2 |
| 1 |
| 2×3 |
| 1 |
| (n-1)n |
=1+（1-
| 1 |
| 2 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| n-1 |
| 1 |
| n |
=1+（1-
| 1 |
| n |
| 1 |
| n |
| 1 |
| 12 |
| 1 |
| 22 |
| 1 |
| 32 |
| 1 |
| n2 |
| 1 |
| 1×2 |
| 1 |
| 2×3 |
| 1 |
| 3×4 |
| 1 |
| n(n+1) |
=1-
| 1 |
| 2 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| 3 |
| 1 |
| 4 |
| 1 |
| n |
| 1 |
| n+1 |
=1-
| 1 |
| n+1 |
∴当n≥2时，则[
| 1 |
| 12 |
| 1 |
| 22 |
| 1 |
| 32 |
| 1 |
| n2 |
故选B．
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