Find the sum of the infinite geometric series. 8 + 2 + 1/2 + 1/8 + Write your answer as an integer or a fraction in simplest form. ______

Identify first term and ratio: Identify the first term (a_1) and the common ratio (r) of the geometric series. The first term a_1 is the first number in the series, which is 8. To find the common ratio r, we divide the second term by the first term. r = a_2/a_1 = 2/8 = 1/4Use sum formula: Use the formula for the sum of an infinite geometric series, which is S = a_1 / (1 - r), where S is the sum, a_1 is the first term, and r is the common ratio. Here, a_1 = 8 and r = 1/4. Now, plug these values into the formula to find the sum. S = 8 / (1 - 1/4)Simplify expression: Simplify the expression to find the sum. S = 8 / (3/4) To divide by a fraction, multiply by its reciprocal. S = 8 * (4/3) S = 32/3

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Find the sum of the infinite geometric series. $\newline$ $8 + 2 + \frac{1}{2} + \frac{1}{8} +$ $\newline$ Write your answer as an integer or a fraction in simplest form. $\newline$ $\_\_$

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Algebra 2

Find the value of an infinite geometric series

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Q. Find the sum of the infinite geometric series.

\newline

8 + 2 + \frac{1}{2} + \frac{1}{8} +

\newline

Write your answer as an integer or a fraction in simplest form.

\newline

\_\_

Identify first term and ratio: Identify the first term $a_1$ and the common ratio $r$ of the geometric series. $\newline$ The first term $a_1$ is the first number in the series, which is $8$ . $\newline$ To find the common ratio $r$ , we divide the second term by the first term. $\newline$ $r = \frac{a_2}{a_1} = \frac{2}{8} = \frac{1}{4}$
Use sum formula: Use the formula for the sum of an infinite geometric series, which is $S = \frac{a_1}{1 - r}$ , where $S$ is the sum, $a_1$ is the first term, and $r$ is the common ratio. $\newline$ Here, $a_1 = 8$ and $r = \frac{1}{4}$ . $\newline$ Now, plug these values into the formula to find the sum. $\newline$ $S = \frac{8}{1 - \frac{1}{4}}$
Simplify expression: Simplify the expression to find the sum. $\newline$ $S = \frac{8}{\frac{3}{4}}$ $\newline$ To divide by a fraction, multiply by its reciprocal. $\newline$ $S = 8 \times \frac{4}{3}$ $\newline$ $S = \frac{32}{3}$