Radius of convergence
In mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, the radius of convergence of a power series is a quantity, either a non-negative real number or ∞, that represents a domain (within the radius) in which the series will converge. Within the radius of convergence, a power series converges absolutely
Absolute convergence
In mathematics, a series of numbers is said to converge absolutely if the sum of the absolute value of the summand or integrand is finite...

 and uniformly on compacta
Compact convergence
In mathematics compact convergence is a type of convergence which generalizes the idea of uniform convergence. It is associated with the compact-open topology.-Definition:...

 as well.