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Find the sum of the infinite geometric series. \newline−4−2−1−12+-4 - 2 - 1 - \frac{1}{2} + \newlineWrite your answer as an integer or a fraction in simplest form. \newline__\_\_

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Q. Find the sum of the infinite geometric series. \newline−4−2−1−12+-4 - 2 - 1 - \frac{1}{2} + \newlineWrite your answer as an integer or a fraction in simplest form. \newline__\_\_
  1. Identify terms and ratio: Identify the first term a1a_1 and the common ratio rr of the geometric series.\newlineThe first term a1a_1 is −4-4.\newlineTo find the common ratio rr, we divide the second term by the first term:\newliner=a2a1=−2−4=12r = \frac{a_2}{a_1} = \frac{-2}{-4} = \frac{1}{2}
  2. Use sum formula: Use the formula for the sum of an infinite geometric series, which is S=a11−rS = \frac{a_1}{1 - r}, where SS is the sum, a1a_1 is the first term, and rr is the common ratio.\newlineWe have a1=−4a_1 = -4 and r=12r = \frac{1}{2}.\newlineNow, calculate the sum:\newlineS=−41−(12)S = \frac{-4}{1 - (\frac{1}{2})}
  3. Simplify and find sum: Simplify the expression to find the sum.\newlineS=−412S = \frac{-4}{\frac{1}{2}}\newlineS=−4×21S = -4 \times \frac{2}{1}\newlineS=−8S = -8

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