In mathematics, the radius of convergence of a power series is the radius of the largest disk in which the series converges. It is either a non-negative real number or ∞. When it is positive, the power series converges absolutely and uniformly on compact sets inside the open disk of radius equal to the radius of convergence, and it is the Taylor series of the analytic function to which it converges.
Read more about Radius Of Convergence: Definition, Finding The Radius of Convergence, Radius of Convergence in Complex Analysis, Convergence On The Boundary, Comments On Rate of Convergence, A Graphical Example, Abscissa of Convergence of A Dirichlet Series