radius of convergence

In mathematics, the radius of convergence is a key concept related to power series. A power series is like an infinite polynomial. For a given power series, there's typically an interval around zero where the series converges to a finite sum. The radius of convergence, denoted by r, is the positive number that defines this interval. Specifically, the series converges for all values of x where the absolute value of x is less than r (i.e., |x| < r). Outside this range, the series diverges. The radius of convergence can often be found using a ratio test on the series' coefficients.12