Consider the following repeating decimal.

$\frac{0.}{b}ar(6)$

$($a$)$ Write the repeating decimal as a geometric series.

${\displaystyle \underset{n=0}{\overset{}{}}}(\frac{6}{{10}^{n+1}})$

$($b$)$ Write the sum of the series as the ratio of two integers.

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