题目内容
数列{
}的前n项和为Sn，则
Sn=______．
| 1 |
| n(n+1) |
| lim |
| n→∞ |
由题意可得an=
=
-
∴Sn=
+
+… +
=1-
+
-
+…+
-
=1-
=
∴
Sn=
=
=1
故答案为：1
| 1 |
| n(n+1) |
| 1 |
| n |
| 1 |
| n+1 |
∴Sn=
| 1 |
| 1×2 |
| 1 |
| 2×3 |
| 1 |
| n(n+1) |
=1-
| 1 |
| 2 |
| 1 |
| 2 |
| 1 |
| 3 |
| 1 |
| n |
| 1 |
| n+1 |
=1-
| 1 |
| n+1 |
| n |
| n+1 |
∴
| lim |
| n→∞ |
| lim |
| n→∞ |
| n |
| n+1 |
| lim |
| n→∞ |
| 1 | ||
1+
|
故答案为：1
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