| 1 | 1 | 1 | ||||
∑n→∞ | = ( | − | ) i co dalej ? wychodzi mi 1 a ma być 1/2 :C | |||
| n2+3n+2 | n+1 | n+2 |
| 1 | ||
∑kn=1 | i liczysz z tego granicę dla k −> +∞ | |
| n2+3n+2 |
| 1 | 1 | 1 | 1 | 1 | 1 | |||||||
( | − | )+( | − | )+...+( | − | ) | ||||||
| 2 | 3 | 3 | 4 | n+1 | n+2 |
| 1 | 1 | n | ||||
Więc zostanie ( | − | )= | , a z tego granica wychodzi 1. Co robię źle ? | |||
| 2 | n+2 | n+2 |
| 1 | 1 | n+2 − 2 | n | ||||
− | = | = | −−−> 0.5 | ||||
| 2 | n+2 | 2*(n+2) | 2(n+2) |
| 1 | 1 | 1 | |||
− | −−−> | + 0 = 0.5 | |||
| 2 | n+2 | 2 |
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | ||||||||
Sn= | − | + | − | + | − | +....− | ||||||||
| 2 | 3 | 3 | 4 | 4 | 5 | n+2 |
| 1 | 1 | |||
Sn= | − | |||
| 2 | n+2 |
| 1 | 1 | 1 | 1 | |||||
limn→∞( | − | )= | −0= | |||||
| 2 | n+2 | 2 | 2 |
| 1 | 1 | n+2−2 | n | 1 | |||||
− | = | = | → | ||||||
| 2 | n+2 | 2(n+2) | 2(n+2) | 2 |
