What is the sum of the infinite series \( S = \sum_{n=0}^{\infty} \frac{1}{3^n} \)?
Show Hint
- \( \frac{3}{2} \)
- \( \frac{1}{2} \)
- 2
- 3
The Correct Option is B
Solution and Explanation
This is a geometric series with the first term \( a = 1 \) and the common ratio \( r = \frac{1}{3} \).
The sum of an infinite geometric series is given by the formula: \[ S = \frac{a}{1 - r}. \]
Substituting \( a = 1 \) and \( r = \frac{1}{3} \): \[ S = \frac{1}{1 - \frac{1}{3}} = \frac{1}{\frac{2}{3}} = \frac{3}{2}. \]
Thus, the sum of the series is \( \frac{3}{2} \).
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