👉 Series mathematics, also known as summation or integral calculus in discrete contexts, is a branch of mathematics that deals with the sum of an infinite number of terms, often represented as a series. It involves adding up values in a sequence where each term is calculated using a specific formula or rule, such as arithmetic series (where each term increases by a constant difference) or geometric series (where each term is a fixed multiple of the previous one). The sum of these terms can be finite or infinite, and understanding how to manipulate and evaluate these series is crucial in various fields like physics, engineering, and finance. For example, the formula for the sum of an arithmetic series \( S_n = \frac{n}{2} (a + l) \) or the geometric series \( S_n = a \frac{1 - r^n}{1 - r} \) for finite sums, and techniques like partial fractions or generating functions for infinite series, are key tools in this area.
