Question

Determine a soma dos termos da P.G infinita (2/3, 3/9, 2/27, 2/81,...)

Answer 1

Explicação passo-a-passo:

Soma da P.G infinita

Temos a₁ e  q

calculando q que é a razão

$a_2\div a_1={3\over9}\div{2\over3}={3\over9}\times{3\over2}={9\over18}={1\over2}\\ \\ a_1={2\over3}\\ \\ q={1\over2}\\ \\ Termo~~geral\\ \\ S_n={a_1\over1-q}\\ \\ S_n={{2\over3}\over1-{1\over2}}\\ \\ S_n={2\over3}\div({1-{1\over2})$

$S_n={2\over3}\div({2-1\over2})\\ \\ S_n={2\over3}\div({1\over2})\\ \\ S_n={2\over3}\times{2\over1}\\ \\ S_n={4\over3}$