Question

Calcular a soma dos termos da P.G. (1, 1/3, 1/9, 1/27, ....)​

Answer 1

Soma dos termos de uma PG infinita

$\huge\boxed{\boxed{\boxed{\boxed{\sf S_n=\dfrac{a_1}{1-q}}}}}$

$\boxed{\begin{array}{l}\sf a_1=1\\\sf q=\dfrac{1}{9}\div\dfrac{1}{3}\\\sf q=\dfrac{1}{\diagup\!\!\!9_3}\cdot\diagup\!\!\!3\\\sf q=\dfrac{1}{3}\\\sf S_n=\dfrac{a_1}{1-q}\\\sf S_n=\dfrac{1}{1-\frac{1}{3}}\\\sf S_n=\dfrac{1}{\frac{2}{3}}\\\sf S_n=1\cdot\dfrac{3}{2}\\\sf S_n=\dfrac{3}{2}\end{array}}$