Find the sum of the infinite geometric series. 1 + 2/3 + 4/9 + 8/27 + Write your answer as an integer or a fraction in simplest form. ______

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Find the sum of the infinite geometric series. 1 + 2/3 + 4/9 + 8/27 +    Write your answer as an integer or a fraction in simplest form. ______

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Identify first term and common ratio: First, we need to identify the first term (a) and the common ratio (r) of the geometric series. The first term a is 1. The common ratio r is the factor by which each term is multiplied to get the next term. In this case, each term is multiplied by 2/3 to get the next term. So, r = 2/3.Use formula for infinite series sum: To find the sum of an infinite geometric series, we use the formula S = a / (1 - r), where S is the sum of the series, a is the first term, and r is the common ratio. This formula only works if the absolute value of r is less than 1, which is true in this case since |2/3| < 1.Plug in values for calculation: Now we can plug the values of a and r into the formula to find the sum of the series. S = 1 / (1 - 2/3)Calculate denominator of fraction: We calculate the denominator of the fraction: 1 - 2/3 = 3/3 - 2/3 = 1/3Find sum by dividing first term: Now we can find the sum S by dividing the first term by the result we just found: S = 1 / (1/3)Multiply to get final sum: To divide by a fraction, we multiply by its reciprocal. So we multiply 1 by the reciprocal of 1/3, which is 3/1 or just 3. S = 1 * 3 = 3

Find the sum of the infinite geometric series. $\newline$ $1 + \frac{2}{3} + \frac{4}{9} + \frac{8}{27} + \dots$ $\newline$ Write your answer as an integer or a fraction in simplest form. $\newline$ ______

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Find the sum of the infinite geometric series. $\newline$ $1 + \frac{2}{3} + \frac{4}{9} + \frac{8}{27} + \dots$ $\newline$ Write your answer as an integer or a fraction in simplest form. $\newline$ ______