range of convergence

In mathematics, convergence describes the property of certain infinite series and functions approaching a limit. This occurs as the number of terms in a series increases or as a variable in a function changes. For example, the function y = 1/x converges to zero as x increases, meaning y gets progressively smaller and approaches zero.

For infinite series, like 1 + x + x² + ... , convergence means the sum approaches a finite value. The range of convergence is the set of values for x for which this happens. For the series 1 + x + x² + ..., the range of convergence is between -1 and +1. Outside this range, the series diverges, meaning its sum grows without bound.12