Question

1)Encontre a soma dos termos da PG (1; 0,5; 0,25; 0,125; …). 2) Determine a soma dos elementos da progressão geométrica dada por (0,3; 0,03; 0,003; 0,0003; ...).​

Answer 1

$> resolucao \\ \\ > resolve \: com \: decimais \: \\ > ou \: transforma \: decimais \: \\ em \: fracoes \: \\ \\ > (1 .\: 0.5 \: 0.25 \: 0.125...) \\ > (1. \frac{1}{2} . \frac{1}{4} . \frac{1}{8} ...) \\ \\ q = \frac{a2}{a1} \\ q = \frac{0.5}{1} \\ q = 0.5 \\ \\ \\ s = \frac{a1}{1 - q} \\ s = \frac{1}{1 - 0.5} \\ s = \frac{1}{0.5} \\ s = 2 \\ \\ > > > > > > > \\ \\ q = \frac{a2}{a1} \\ q = \frac{1}{2} \div 1 \\ q = \frac{1}{2} \times 1 \\ q = \frac{1}{2} \\ \\ \\ s = \frac{1}{1 - \frac{1}{2} } \\ s = \frac{1}{ \frac{1}{2} } \\ s = 1 \times \frac{2}{1} \\ s = \frac{2}{1} \\ s = 2 \\ \\ \\ > > > > > > > > > > > > \\ \\ > (0.3 \: 0.03 \: 0.003 \: 0.0003....) \\ > ( \frac{3}{10} . \: \frac{3}{100} .\: \frac{3}{1000 } .\: \frac{3}{10000} ) \\ \\ q = \frac{a2}{a1} \\ q = \frac{0.03}{0.3} \\ q = 0.1 \\ \\ s = \frac{a1}{1 - q} \\ s = \frac{0.3}{1 - 0.1} \\ s = \frac{0.3}{0.9} \\ s = 0.33333... \\ \\ > > > > > > > > \\ \\ q = \frac{a2}{a1} \\ q = \frac{3}{100} \div \frac{3}{10} \\ q = \frac{3}{100} \times \frac{10}{3} \\ q = \frac{30}{300} \\ q = \frac{1}{10} \\ \\ \\ s \frac{a1}{1 - q} \\ s = \frac{3}{10} \div 1 - \frac{1}{10} \\ s = \frac{3}{10} \div \frac{9}{10} \\ s = \frac{3}{10} \times \frac{10}{9} \\ s = \frac{30}{90} \\ s = \frac{1}{3} \\ \\ \\ \\ \\ > > > > > > > > > > >$