Determining the Radius and Interval of Convergence for a Power Series

Determining the radius and interval of convergence for a power series is a fundamental task in calculus and mathematical analysis. This process involves investigating the behavior of a series representation of a function to ascertain the range of values for which the series converges. By employing various convergence tests such as the ratio test or the root test, mathematicians can ascertain the radius of convergence, which represents the distance from the center of convergence to the nearest point where the series diverges. Understanding these concepts is crucial for applications in fields like engineering, physics, and economics.