Question

calcule a soma dos oito primeiros termos da pg (81,27,9...)

Answer 1

$a_1 = 81 \\ \\ q = \dfrac{1}{3} \\ \\ n = 8 \\ \\ S_n = \dfrac{a_1(q^n-1)}{q-1} \\ \\ S_8 = \dfrac{81((\frac{1}{3})^8-1)}{\frac{1}{3}-1}$

$S_8 = \dfrac{81(\frac{1}{6561}-1)}{\frac{1-3}{3}} \\ \\ S_8 = \dfrac{81(\frac{1-6561}{6561})}{\frac{-2}{3}}$

$S_8 = \dfrac{-3}{2}\cdot81(\frac{-6560}{6561}) = \dfrac{(-3)(81)(-6560)}{(2)(6561)} = \dfrac{(1)(1)(3280)}{(1)(27)} = \dfrac{3280}{27}$