| 1 | 2 | n | ||||
limn→∞( | + | +...+ | ) | |||
| (√n4+1) | (√n4+2) | (√n4+n) |
| 1+2+...+(n−1) | 1 | 2 | n | ||||
≤ ( | + | +...+ | ) ≤ | ||||
| √n4 | (√n4+1) | (√n4+2) | (√n4+n) |
| 1+2+..+n | ||
| √n4 |
| n2 | 1 | 1 | ||||
limn→∞ | * | = | ||||
| 2 | n2 | 2 |
| n2+n | 1 | 1 | ||||
limn→∞ | * | = | ||||
| 2 | n2 | 2 |
| 1 | 2 | n | ||||
na mocy tw. o 3 ciągach limn→∞( | + | +...+ | ) = | |||
| (√n4+1) | (√n4+2) | (√n4+n) |
| 1 | ||
| 2 |
| 1+2+...+n | (1+n)n | ||
= | |||
| √n4+1 | 2√n4+1 |
| (1+n)n | |
| 2√n4+n |
| 1 | ||
więc g = | ||
| 2 |