| 3 | ||
Nieskończony ciąg geometryczny (an) spełnia warunki: a1= | oraz | |
| 5 |
| 4 | 4 | |||
an+2= | *an+1− | *an dla n ≥ 1 . Suma wszystkich wyrazów tego ciągu jest równa | ||
| 3 | 9 |
| 3 | ||
a1= | ||
| 5 |
| 4 | 4 | 3 | ||||
a1*q2= | *a1*q− | * | ||||
| 3 | 9 | 5 |
| 4 | 4 | |||
a1*q2= | *a1*q− | |||
| 3 | 15 |
| 3 | 4 | 3 | 4 | ||||
*q2= | * | *q− | |||||
| 5 | 3 | 5 | 15 |
| 3 | 4 | 4 | |||
*q2= | *q− | ||||
| 5 | 5 | 15 |
| 3 | 4 | 4 | |||
q2− | q+ | =0 / * 15 | |||
| 5 | 5 | 15 |
| 2 | ||
q= | ||
| 3 |
| 3 | 9 | ||||||||||
S= | = | *3= | ||||||||||
| 5 | 5 |