Question

determine a soma dos termos da p.g. infinita ( 2/3, 2/9, 2/27,…)

Answer 1

$> resolucao \\ \\ \geqslant progressao \: \: geometrica \\ \\ q = \frac{a2}{a1} \\ \\ q = \frac{ \frac{2}{9} }{ \frac{2}{3} } \\ \\ q = \frac{2}{9} \times \frac{3}{2} \\ \\ q = \frac{6 \div 6}{18 \div 6} \\ \\ q = = \frac{1}{3} \\ \\ = = = = = = = = = = = = = = = = = = = = = = \\ \\ \\ sn = \frac{a1}{1 - q} \\ \\ sn = \frac{ \frac{2}{3} }{1 - \frac{1}{3} } \\ \\ sn = \frac{ \frac{2}{3} }{ \frac{2}{3} } \\ \\ sn = \frac{2}{3} \times \frac{3}{2} \\ \\ sn = \frac{6}{6} \\ \\ sn = 1 \\ \\ \\ \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \leqslant \geqslant \geqslant \geqslant$