Question

can anyone explain me the radius of convergence of power series?

Answer 1

The radius of convergence of a power series is a way to measure the size of the set of numbers of the variable, say X, for which the power series actually converges. For example, the power series for e^x includes all reals, so the radius of convergence is infinite. However, some series may only converge for -1<x<1, so the radius of convergence in this case is 1. This is found by using the ratio test.