in mathematics, property (exhibited by certain infinite series and functions (function)) of approaching a limit more and more closely as an argument (variable) of the function increases or decreases or as the number of terms of the series increases.

For example, the function y=1/x converges to zero as x increases. Although no finite value of x will cause the value of y to actually become zero, the limiting value of y is zero because y can be made as small as desired by choosing x large enough. The line y=0 (the x-axis) is called an asymptote of the function.

Similarly, for any value of x between (but not including) −1 and +1, the series 1+x+x²+⋯+xⁿ converges toward the limit 1/(1−x) as n, the number of terms, increases. The interval −1\\<x\\<1 is called the range of convergence of the series; for values of x outside this range, the series is said to diverge.