ПОВТОРЕННЯ НАВЧАЛЬНОГО МАТЕРІАЛУ » §.3 (3.1)

3) У геометричній прогресії (bn): 1. b1 = 12, b4 = 3/2; q – ? S7 – ? b4 = b1q3. 12 • q3 = 3/2; q3 = 3/24; q3 = 1/8; 1 = ± 1/2; q = 1/2 : S7 = (b_1 (q^7- 1))/(q-1) = (12((1/2 )^7- 1))/(1/2- 1) = (24(1/128- 1))/(-1) = 24(1 – 1/128) = 24 • 127/128 = 23104/128 = 2326/32 = 2313/16. q = –1/2 : S7 = (12(-1/128- 1))/(-1/2- 1) = (12 • 129/128)/(3/2) = (24 •129)/(3 •128) = 81/16;