Question

1) O conjunto solução da equação x+x/3+x/9+⋯=9 é: (A) {2} (B) {3} (C) {4} (D) {5} (E) {6}

Answer 1

$\displaystyle \text x+\frac{\text x }{3}+\frac{\text x}{9}+ \ ... \ =9 \\\\\\ \underline{\text{Soma dos infinitos termos de uma PG, onde}}: \\\\ \text a_1 = \text x \ \ ; \ \ \text q= \frac{1}{3} \ \ ; \ \ \text S_\infty = 9 \\\\\\ \text S_\infty = \frac{\text a_1}{1-\text q} \\\\\\ 9=\frac{\text x}{\displaystyle 1-\frac{1}{3}}\\\\\\ 9=\frac{\text x}{\displaystyle \frac{2}{3}} \\\\\\ \text x = \frac{9.2}{3} \\\\\\ \huge\boxed{\text x=6\ }\checkmark$