Geometric series

A geometric series is a series of terms that have a constant ratio between successive terms. It is formed from a geometric sequence, which is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

The series given is a geometric series where the first term \( a \) is \( \frac{1}{2} \) and the common ratio \( r \) is \( \frac{1}{2} \).

We can represent the series \( S = \frac{1}{2} - \frac{1}{4} + \frac{1}{8} - \frac{1}{16} + \cdots \) more clearly by recognizing it as an infinite geometric series. ### Step 1: Identify the First Term and the Common Ratio The first term \( a \) of the series is \( \frac{1}{2} \).