Series Expansions

Series expansions are mathematical tools that express complex functions as sums of simpler terms, often involving powers of a variable. They help approximate functions that are difficult to compute directly by breaking them down into an infinite or finite series of easier-to-understand components. For example, a function like sine or exponential can be represented as a series, making calculations and analysis more manageable. These expansions are widely used in science and engineering for modeling, solving equations, and understanding behavior near specific points, providing a powerful way to analyze and approximate a wide range of functions.