Question

What is the sum of the infinite series \( S = \sum_{n=0}^{\infty} \frac{1}{3^n} \)?

• A. \( \frac{3}{2} \)
• B. \( \frac{1}{2} \)
• C. 2
• D. 3

Hint:

For an infinite geometric series with \( |r|<1 \), the sum is given by \( S = \frac{a}{1 - r} \).

Answer 1

The Correct Option is B

This is an infinite geometric series with an initial term \( a = 1 \) and a constant ratio \( r = \frac{1}{3} \). The sum is calculated using the formula \( S = \frac{a}{1 - r} \). With \( a = 1 \) and \( r = \frac{1}{3} \), the sum is \( S = \frac{1}{1 - \frac{1}{3}} = \frac{1}{\frac{2}{3}} = \frac{3}{2} \). Consequently, the series' sum is \( \frac{3}{2} \).