Question

A soma dos termos ( 9, 3,..., 1/81)

Answer 1

Sn = a1( 1 - qⁿ) / 1 - q

vamos saber quantos termos tem a sequência

an = a1 . qⁿ⁻¹
1/81 = 9 . (1/3)ⁿ⁻¹
(1/3)ⁿ⁻¹ =  1/81 . 1/9
(1/3)ⁿ⁻¹ = 1/729
(1/3)ⁿ⁻¹ = (1/3)⁶
n - 1 =  6
n = 6 + 1
n = 7

S7 = 9( 1 - (1/3)⁷ ) / 1 - 1/3
S7 = 9 - (9/3⁷ ) / 3/3 - 1/3
S7 = 9 - (3²/3⁷) / 2/3
S7 = 9 - 3⁻⁵ / 2/3
S7 = 9 - 1/3⁵ / 2/3
S7 = 9 - 1/ 243   / 2/3
S7 = 2187/243 - 1/243  / 2/3
S7 = 2186 / 243   / 2/3
S7 = 2186 . 3  / 243 . 2
S7 = 6558 / 486 (÷2)
S7 = 3279 / 243 (÷3)
S7 =1093 / 81