Find the sum of the infinite geometric series. -1 - 1/2 - 1/4 - 1/8 + Write your answer as an integer or a fraction in simplest form. ______

Identify first term and common ratio: To find the sum of an infinite geometric series, we need to identify the first term (a) and the common ratio (r) of the series. The first term is the first number in the series, and the common ratio is the factor by which we multiply to get from one term to the next. In this series, the first term a = -1, and the common ratio r = 1/2 (because each term is half of the previous term).Apply sum formula: The sum S of an infinite geometric series with |r| < 1 can be found using the formula S = a / (1 - r), where a is the first term and r is the common ratio. Let's apply this formula to our series.Substitute values into formula: Substitute the values of a and r into the formula: S = -1 / (1 - 1/2)Calculate denominator: Now, calculate the denominator: 1 - 1/2 = 1/2Calculate sum: Next, calculate the sum using the values: S = -1 / (1/2)Multiply by reciprocal: To divide by a fraction, we multiply by its reciprocal. So, we multiply -1 by 2 (the reciprocal of 1/2): S = -1 * 2Perform final multiplication: Perform the multiplication to find the sum: S = -2

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Find the sum of the infinite geometric series. $\newline$ $-1 - \frac{1}{2} - \frac{1}{4} - \frac{1}{8} +$ $\newline$ Write your answer as an integer or a fraction in simplest form. $\newline$ $\_\_$

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Precalculus

Find the value of an infinite geometric series

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Q. Find the sum of the infinite geometric series.

\newline

-1 - \frac{1}{2} - \frac{1}{4} - \frac{1}{8} +

\newline

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

\newline

\_\_

Identify first term and common ratio: To find the sum of an infinite geometric series, we need to identify the first term $a$ and the common ratio $r$ of the series. The first term is the first number in the series, and the common ratio is the factor by which we multiply to get from one term to the next. $\newline$ In this series, the first term $a = -1$ , and the common ratio $r = \frac{1}{2}$ (because each term is half of the previous term).
Apply sum formula: The sum $S$ of an infinite geometric series with |r| < 1 can be found using the formula $S = \frac{a}{1 - r}$ , where $a$ is the first term and $r$ is the common ratio. $\newline$ Let's apply this formula to our series.
Substitute values into formula: Substitute the values of $a$ and $r$ into the formula: $S = -\frac{1}{1 - \frac{1}{2}}$
Calculate denominator: Now, calculate the denominator: $\newline$ $1 - \frac{1}{2} = \frac{1}{2}$
Calculate sum: Next, calculate the sum using the values: $\newline$ $S = -\frac{1}{\left(\frac{1}{2}\right)}$
Multiply by reciprocal: To divide by a fraction, we multiply by its reciprocal. So, we multiply $-1$ by $2$ (the reciprocal of $\frac{1}{2}$ ): $\newline$ $S = -1 \times 2$
Perform final multiplication: Perform the multiplication to find the sum: $\newline$ $S = -2$