| 1 |
| n2+n+n |
| 1 |
| n2+n+i |
| 1 |
| n2+n+1 |
故
| 1+2+…+n |
| n2+n+n |
| ||
| i＝1 |
| i |
| n2+n+i |
| 1+2+…+n |
| n2+n+1 |
又：
| lim |
| n→∞ |
| 1+2+…+n |
| n2+n+n |
| lim |
| n→∞ |
| ||
| n2+n+n |
| 1 |
| 2 |
| lim |
| n→∞ |
| 1+2+…+n |
| n2+n+1 |
| lim |
| n→∞ |
| ||
| n2+n+1 |
| 1 |
| 2 |
由夹逼准则有：
| lim |
| n→∞ |
| ||
| i＝1 |
| i |
| n2+n+i |
| 1 |
| 2 |
| lim |
| n→∞ |
| 1 |
| n2+n+1 |
| 2 |
| n2+n+2 |
| n |
| n2+n+n |
| 1 |
| n2+n+n |
| 1 |
| n2+n+i |
| 1 |
| n2+n+1 |
| 1+2+…+n |
| n2+n+n |
| ||
| i＝1 |
| i |
| n2+n+i |
| 1+2+…+n |
| n2+n+1 |
| lim |
| n→∞ |
| 1+2+…+n |
| n2+n+n |
| lim |
| n→∞ |
| ||
| n2+n+n |
| 1 |
| 2 |
| lim |
| n→∞ |
| 1+2+…+n |
| n2+n+1 |
| lim |
| n→∞ |
| ||
| n2+n+1 |
| 1 |
| 2 |
| lim |
| n→∞ |
| ||
| i＝1 |
| i |
| n2+n+i |
| 1 |
| 2 |