13 Consider the Geometric series given by \( S=\frac{12}{2} \) Calculate the value of \( S \).

The geometric series given by \( S = \frac{12}{2} \) simplifies to \( S = 6 \). This value represents the sum of the series based on the relationship defined by its terms. Geometric series are fun because they pop up in everything from calculating interest on loans to predicting the number of views on viral videos! If you ever find yourself confused with geometric series, remember that the key to solving them is the formula for the sum, which is \( S_n = a \frac{1 - r^n}{1 - r} \) for finite series, where \( a \) is the first term and \( r \) the common ratio. Common mistakes often include mixing up terms or not correctly identifying the ratio! Always double-check those values!