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Find the sum of the infinite geometric series.\newline4+2+1+12+…4 + 2 + 1 + \frac{1}{2} + \dots\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.\newline4+2+1+12+…4 + 2 + 1 + \frac{1}{2} + \dots\newlineWrite your answer as an integer or a fraction in simplest form.\newline__\_\_
  1. Identify Terms: Identify the first term a1a_1 and the common ratio rr of the geometric series.\newlineThe first term a1a_1 is the first number in the series, which is 44.\newlineTo find the common ratio rr, we divide the second term by the first term.\newliner=a2a1=24=12r = \frac{a_2}{a_1} = \frac{2}{4} = \frac{1}{2}
  2. Calculate Common Ratio: 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, plug these values into the formula to find the sum.\newlineS=41−12S = \frac{4}{1 - \frac{1}{2}}
  3. Use Sum Formula: 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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