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Find the sum of the infinite geometric series.\newline2+1+12+14+…2 + 1 + \frac{1}{2} + \frac{1}{4} + \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.\newline2+1+12+14+…2 + 1 + \frac{1}{2} + \frac{1}{4} + \dots\newlineWrite your answer as an integer or a fraction in simplest form.\newline__\_\_
  1. Substitute values into formula: Now that we have the first term and the common ratio, we can use the formula for the sum of an infinite geometric series:\newlineS=a11−rS = \frac{a_1}{1 - r}\newlineSubstitute the values of a1a_1 and rr into the formula:\newlineS=21−(12)S = \frac{2}{1 - (\frac{1}{2})}
  2. Perform calculation: Perform the calculation inside the parentheses first:\newline1−(12)=121 - \left(\frac{1}{2}\right) = \frac{1}{2}\newlineNow, substitute this value back into the formula:\newlineS=2(12)S = \frac{2}{\left(\frac{1}{2}\right)}
  3. Divide by reciprocal: To divide by a fraction, multiply by its reciprocal:\newlineS=2×(21)S = 2 \times \left(\frac{2}{1}\right)\newlineS=4S = 4

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