Question

a fracao geratriz de 0,5555555...é​

Answer 1

Caso tenha problemas para visualizar a resposta experimente abrir pelo navegador https://brainly.com.br/tarefa/33253061

===============================================================

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

$\sf{\underbrace{0,555...=0,5....+0,05....+0,005....}_{soma~dos~termos~da~PG~infinita}}\\\sf{a_1=0,5=\frac{5}{10}}\\\sf{a_2=0,05=\frac{5}{100}}\\\sf{q=\dfrac{a_2}{a_1}}$

$\sf{q=\dfrac{\frac{5}{100}}{\frac{5}{10}}}\\\sf{q=\dfrac{\diagup\!\!\!5}{10\diagup\!\!\!0}\cdot\dfrac{1\diagup\!\!\!0}{\diagup\!\!\!5}}\\\sf{q=\dfrac{1}{10}}$

$\sf{S_n=\dfrac{\frac{5}{10}}{1-\frac{1}{10}}}\\\sf{S_n=\dfrac{\frac{5}{10}}{\frac{9}{10}}}\\\sf{S_n=\dfrac{5}{\diagdown\!\!\!\!\!\!10}\cdot\dfrac{\diagdown\!\!\!\!\!\!10}{9}}\\\huge\boxed{\boxed{\boxed{\boxed{\sf{S_n=\dfrac{5}{9}}}}}}$

=================================================================

Outra resolução:

$\sf{x=0,555...\cdot10}}\\\sf{10x=5,555....}\\-\underline{\begin{cases}\sf{10x=5,\diagup\!\!\!5\diagup\!\!\!5\diagup\!\!\!5...}\\\sf{x=0,\diagup\!\!\!5\diagup\!\!\!5\diagup\!\!\!5...}\end{cases}}\\\sf{9x=5}\\\huge\boxed{\boxed{\boxed{\boxed{\boxed{\sf{x=\dfrac{5}{9}\checkmark}}}}}}$