CONVERGENCE

in mathematics, property (exhibited by certain series and functions) of approaching a limit more and more closely as an argument of the function increases or decreases or as the number of terms of the series increases. For example, the function y = 1/x converges on zero as x increases. Although no finite value of x will cause the value of y actually to 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