Question

A solução da equação a seguir é: x+ x /3 + x/ 9 +...=9

Answer 1

$\displaystyle \sf x +\frac{x}{3}+\frac{x}{9}+\ ...\ = 9 \\\\ PG : \\\\ a_1 = x \ \ ; \ \ q = \frac{1}{3} \ \ ;\ \ S_\infty =9 \\\\\\ S_\infty = \frac{a_1}{1-q} \\\\ \underline{Da{\'i}}}: \\\\ 9 = \frac{x}{1-\frac{1}{3}} \to 9 = \frac{x}{\frac{2}{3}} \\\\\\ x = 9\cdot \frac{2}{3} \to x = 3\cdot 2 \\\\ \huge\boxed{\sf x = 6 }\checkmark$