3. Последовательность (аn) — геометрическая прогрессия. Найдите:

a) S₅ = -45 * (1 - (1/3)⁵) / (1 - 1/3) = -45 * (1 - 1/243) / (2/3) = -45 * (242/243) * (3/2) = -135/2 * 242/243 = -15 * 242 / 27 = -5 * 242 / 9 = -1210/9.

в) S₆ = 4 * (1 - (-6)⁶) / (1 - (-6)) = 4 * (1 - 46656) / 7 = 4 * (-46655) / 7 = -186620 / 7.

б) S₄ = 243 * (1 - (1/3)⁴) / (1 - 1/3) = 243 * (1 - 1/81) / (2/3) = 243 * (80/81) * (3/2) = 3 * 80 * 3 / 2 = 360.

г) S₅ = 216√6 * (1 - (√6)⁵) / (1 - √6) = 216√6 * (1 - 36√6) / (1 - √6) = 216√6 * (1 - 36√6) * (1 + √6) / (1 - 6) = 216√6 * (1 + √6 - 36√6 - 36*6) / (-5) = 216√6 * (1 - 35√6 - 216) / (-5) = 216√6 * (-215 - 35√6) / (-5) = 216√6 * (215 + 35√6) / 5 = 216√6 * (43 + 7√6) = 9288√6 + 216 * 7 * 6 = 9288√6 + 9072.