Find the sum of the infinite geometric series: \(3, 6, 12, 24, ...\)
Substituting the given values into the formula, we have \(S = \frac{3}{1 - 2}\)
Step 1 :First, we need to identify the common ratio of the geometric series. We do this by dividing the second term by the first term, and we find that the common ratio \(r = \frac{6}{3} = 2\)
Step 2 :Next, we use the formula for the sum of an infinite geometric series, which is \(S = \frac{a}{1 - r}\), where \(a\) is the first term and \(r\) is the common ratio.
Step 3 :Substituting the given values into the formula, we have \(S = \frac{3}{1 - 2}\)