Геометрическая прогрессия Дано: b1=1/2 n=7 Sn=127/128 Найти: q-? bn-?

S_n = (b_1 - b_1 * q^ (n-1) * q) / (q - 1) = (b_1 - b_n * q) / (q - 1);

b_1 = 1/2

b_n = (1/2) ^7

127/128 = (1/2 - 127q/128) / (1 - q);

(127/128 - (64 - q) / 128 (1-q)) : ((127 - 127q - 64 + q) / 128 (1-q)) = 0

63 - 126q = 0 q = 1/2 b_n = b_1 * q^ (n-1)

(1/2) ^7 = (1/2) * (1/2) ^ (n-1); (1/2) ^7 = (1/2) ^n; n = 7

Ответ: q = 1/2; n = 7