b1 = 512; bn = 1; Sn = 1023;
Sn = (bn · q - b1)/(q - 1)
1023 = (q - 512)/(q - 1)
1023q - 1023 = q - 512
1022q = 511
q = 1/2
bn = b1 · q^(n - 1) 1 = 512 · (1/2)^(n -1) 1/512 = 1/2^(n - 1)
1/2^9 = 1/2^(n - 1)
9 = n - 1
n = 10
Ответ: n = 10; q = 1/2
Формулу разности квадратов.
(x + y + z)(x - y - z) = (x + (y + z))(x - (y + z)) = x² - (y + z)²
Сosa=4/5
sina=+-√(1-cos²a)=+-√(1-16/25)=+-√(9/25)=+-3/5
tga=sina/cosa
tga=+-3/5:4/5=+-3/5*5/4=+-3/4