Find the sum of the geometric series.
$11 + \frac{11}{2} + \frac{11}{4} + \frac{11}{8} + \dots$
The sum of the geometric series is (Type an integer or a simplified fraction.)

Answer

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Answer

Final Answer: The sum of the geometric series is $22$

Steps

Step 1 ：Given the geometric series $11 + \frac{11}{2} + \frac{11}{4} + \frac{11}{8} + \dots$

Step 2 ：We recognize that this is a geometric series with the first term $a = 11$ and the common ratio $r = \frac{1}{2}$

Step 3 ：The sum of an infinite geometric series can be found using the formula $S = \frac{a}{1 - r}$

Step 4 ：Substituting the given values into the formula, we get $S = \frac{11}{1 - \frac{1}{2}} = 22$

Step 5 ：Final Answer: The sum of the geometric series is $22$