Express each of the repeating decimals in Exercises 71–78 as a geometric series and as the quotient of two integers reduced to lowest terms.
$2.2131313 . . .$

Question

Express each of the repeating decimals in Exercises 71–78 as a geometric series and as the quotient of two integers reduced to lowest terms.
$2.2131313 . . .$

Accepted Answer

The given repeating decimal as a geometric series is $\frac{22 + \sum_{k = 0}^{\infty} 0.13 {(0.01)}^{k}}{10},$ and as the quotient of two integers reduced to lowest terms is $\frac{2191}{990} .$

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Express each of the repeating decimals in Exercises 71–78 as a geometric series and as the quotient of two integers reduced to lowest terms.
$2.2131313 . . .$

Step by Step Solution

Step 1. Given Information.

Step 2. Express the repeating decimal as a geometric series.

Step 3. Express the repeating decimal as the quotient of two integers reduced to the lowest terms.

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Calculus

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Express each of the repeating decimals in Exercises 71–78 as a geometric series and as the quotient of two integers reduced to lowest terms.2.2131313 ...

Step by Step Solution

Step 1. Given Information.

Step 2. Express the repeating decimal as a geometric series.

Step 3. Express the repeating decimal as the quotient of two integers reduced to the lowest terms.

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Express each of the repeating decimals in Exercises 71–78 as a geometric series and as the quotient of two integers reduced to lowest terms.
$2.2131313 . . .$