| 1 | 1 | 1 | 1 | 1 | 1 | |||||||
= | − | + | − | + | − | + ...... | ||||||
| 2 | 4 | 4 | 6 | 6 | 8 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | ||||||||
2*( | ) = | − | ⇔ ( | ) = | *( | − | ) , | |||||||
| n(n+2) | n | n+2 | n(n+2) | 2 | n | n+2 |
| 1 | ||
czyli całą prawą strone mnożysz jeszcze przez : | ||
| 2 |
| 1 | A | B | 2An+2A+2Bn | (2A+2B)n+2A | |||||
= | + | = | = | ||||||
| 2n(2n+2) | 2n | 2n+2 | 2n(2n+2) | 2n(2n+2) |
| ⎧ | A+2B=0 | |
| ⎜ | ||
| ⎨ | ||
| ⎩ | 2A=1 |
| ⎧ | A=0.5 | |
| ⎜ | ||
| ⎨ | ||
| ⎩ | 1+2B=0 |
| ⎧ | A=0.5 | |
| ⎜ | ||
| ⎨ | ||
| ⎩ | B=−0.5 |
| 1 | 1 | 1 | |||
= | − | ||||
| 2n(2n+2) | 4n | 4n+4 |
| 1 | ||
Ale koniec koncow wychodzi tak jak u Jerzego, tyle że nie trzeba mnożyć przez | .  | |
| 2 |
| 1 | 1 | 1 | 1 | 1 | |||||
− | + | − | + | −... | |||||
| 4 | 8 | 8 | 12 | 12 |