Question

10. You can express \( 0 . \overline{5184} \) as an infinite geometric series. \[ \begin{aligned} 0 . \overline{5184} & =0.584584584 \cdots \\ & =0.584+0.000584+0.000000584+\cdots \end{aligned} \] Determine the sum of the series.

          10. You can express \( 0 . \overline{5184} \) as an infinite geometric series.
\[
\begin{aligned}
0 . \overline{5184} & =0.584584584 \cdots \\
& =0.584+0.000584+0.000000584+\cdots
\end{aligned}
\]

Determine the sum of the series.

10. You can express 0 . 5184 as an infinite geometric series.

0 . 5184 =0.584584584 ⋯
=0.584+0.000584+0.000000584+⋯

Determine the sum of the series.

Added by Jennifer W.

Precalculus

Raymond A. Barnett, Michael R. Ziegler,… 7th Edition

Chapter 11

Instant Answer

Solved by Expert Aarti Kumari

Step 1

The first term \(a\) is the initial number in the series, which is \(0.584\). The series progresses by multiplying this term by a certain factor to get the next term. To find the common ratio \(r\), observe how each term is related to the previous one. Show more…

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10. You can express \( 0 . \overline{5184} \) as an infinite geometric series. \[ \begin{aligned} 0 . \overline{5184} & =0.584584584 \cdots \\ & =0.584+0.000584+0.000000584+\cdots \end{aligned} \] Determine the sum of the series.