Question

A fração geratriz da dizima periodica 0,888... é

Answer 1

Resposta:

8/9

Explicação passo-a-passo:

0,888... ⇒ 8/9

Answer 2

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$\Large\boxed{\sf{\underline{Soma~dos~termos~da~PG~infinita}}}\\\huge\boxed{\boxed{\boxed{\boxed{\boxed{\sf S_n=\dfrac{a_1}{1-q}}}}}}$

$\sf0,888...=\underbrace{0,8...+0,08...+0,008....+....}_{soma~dos~termos~da~PG~infinita}\\\sf a_1=0,8=\frac{8}{10}~a_2=0,08=\frac{8}{100}$

$\sf q=\dfrac{a_2}{a_1}\\\sf q=\dfrac{\frac{8}{100}}{\frac{8}{10}}\\\sf q=\dfrac{\diagup\!\!\!8}{10\diagup\!\!\!0}\cdot\dfrac{1\diagup\!\!\!0}{\diagup\!\!\!8}=\dfrac{1}{10}$

$\sf S_n=\dfrac{a_1}{1-q}\\\sf S_n=\dfrac{\frac{8}{10}}{1-\frac{1}{10}}\\\sf S_n=\dfrac{\frac{8}{10}}{\frac{10-1}{10}}\\\sf S_n=\dfrac{\frac{8}{10}}{\frac{9}{10}}\\\sf S_n=\dfrac{8}{\diagup\!\!\!\!\!10}\cdot\dfrac{\diagup\!\!\!\!\!10}{9}\\\huge\boxed{\boxed{\boxed{\boxed{\sf S_n=\dfrac{8}{9}\checkmark}}}}$