x
force: Dany jest ciąg an=3√4*9√4*p27{4}*...*p3n{4} wyznacz wzor oglony ciagu bn=log8an n∊N+
29 wrz 22:24
Godzio:
a
n =
3√4 *
9√4 *
27√4 * ... *
3n√4 = 4
1/3 + 1/9 + ... + 1/(3n) =
= 4
1/3 * (1 − (1/3)n)/(1 − 1/3) = 4
1/3 * 3/2 * (1 − 1/3n) = 4
(1 − 1/3n)/2
| | | |
bn = log84(1 − 1/3n)/2 = |
| * log84 = |
| | 2 | |
| | | | 2 | | 1 | | 1 | |
= |
| * |
| = |
| − |
| |
| | 2 | | 3 | | 3 | | 3n + 1 | |
29 wrz 23:12