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. ______

Calculate Rolls Needed: To solve this problem, we need to determine how many rolls of tape the electrician needs to order to have 8,000 centimeters of electrical tape, given that each roll contains 2,000 centimeters of tape. We will use division to calculate the number of rolls required.Division Calculation: We divide the total amount of tape needed by the amount of tape on each roll to find the number of rolls needed. Calculation: 8,000 cm ÷ 2,000 cm/roll = 4 rollsInfinite Geometric Series: The given series is an infinite geometric series with the first term a = 1 and the common ratio r = 1/2. To find the sum of an infinite geometric series, we use the formula S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio. This formula is only valid if the absolute value of r is less than 1, which is true in this case since |1/2| < 1.Substitute Values: We substitute the values of a and r into the formula to find the sum of the series. Calculation: S = 1 / (1 - 1/2) = 1 / (1/2) = 1 * (2/1) = 2

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Find the sum of the infinite geometric series. $\newline$ $1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots$ $\newline$ 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} + \dots

\newline

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

\newline

\_\_

Calculate Rolls Needed: To solve this problem, we need to determine how many rolls of tape the electrician needs to order to have $8,000$ centimeters of electrical tape, given that each roll contains $2,000$ centimeters of tape. We will use division to calculate the number of rolls required.
Division Calculation: We divide the total amount of tape needed by the amount of tape on each roll to find the number of rolls needed. $\newline$ Calculation: $8,000 \, \text{cm} \div 2,000 \, \text{cm/roll} = 4 \, \text{rolls}$
Infinite Geometric Series: The given series is an infinite geometric series with the first term $a = 1$ and the common ratio $r = \frac{1}{2}$ . To find the sum of an infinite geometric series, we use the formula $S = \frac{a}{(1 - r)}$ , where $S$ is the sum, $a$ is the first term, and $r$ is the common ratio. This formula is only valid if the absolute value of $r$ is less than $1$ , which is true in this case since |\frac{1}{2}| < 1.
Substitute Values: We substitute the values of $a$ and $r$ into the formula to find the sum of the series. $\newline$ Calculation: $S = \frac{1}{(1 - \frac{1}{2})} = \frac{1}{(\frac{1}{2})} = 1 \times (\frac{2}{1}) = 2$