题目内容
若
=
，则a=
| lim |
| n→∞ |
| a(1+2+…n) |
| 2n2-5n+3 |
| 1 |
| 2 |
2
2
．分析：先由等差数列的前n项和公式，把
等价转化为
，再由极限的运算法则进行求解．
| lim |
| n→∞ |
| a(1+2+3+…+n) |
| 2n2-5n+3 |
| lim |
| n→∞ |
a•
| ||
| 2n2-5n+3 |
解答：解：∵
=
=
=
=
．
∴a=2．
故答案为：2．
| lim |
| n→∞ |
| a(1+2+3+…+n) |
| 2n2-5n+3 |
=
| lim |
| n→∞ |
a•
| ||
| 2n2-5n+3 |
=
| lim |
| n→∞ |
| ||||
| 2n2-5n+3 |
=
| a |
| 4 |
=
| 1 |
| 2 |
∴a=2．
故答案为：2．
点评：本题考查极限的逆运算，是基础题．解题时要认真审题，仔细解答，注意等差数列的前n项和公式的灵活运用．
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