题目内容
设f(n)=
+
+
+…+
，则
n2[f(n+1)-f(n)]=______．
| 1 |
| n+1 |
| 1 |
| n+2 |
| 1 |
| n+3 |
| 1 |
| 2n |
| lim |
| n→+∞ |
由题意可得，f（n+1）-f（n）=（
+
+
+…+
）-（
+
+
+…+
）=
+
-
，
则
n2[f(n+1)-f(n)]=
n2（
+
-
）=
（n2•
）=
（
）=
（
）=
=
，
故答案为
．
| 1 |
| n+2 |
| 1 |
| n+3 |
| 1 |
| n+4 |
| 1 |
| 2n+2 |
| 1 |
| n+1 |
| 1 |
| n+2 |
| 1 |
| n+3 |
| 1 |
| 2n |
| 1 |
| 2n+1 |
| 1 |
| 2n+2 |
| 1 |
| n+1 |
则
| lim |
| n→+∞ |
| lim |
| n→+∞ |
| 1 |
| 2n+1 |
| 1 |
| 2n+2 |
| 1 |
| n+1 |
| lim |
| n→+∞ |
| 1 |
| (2n+1)(2n+2) |
| lim |
| n→+∞ |
| n2 |
| 4n2+6n+2 |
| lim |
| n→+∞ |
| 1 | ||||
4+
|
| 1 |
| 4+0+0 |
| 1 |
| 4 |
故答案为
| 1 |
| 4 |
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