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Feb 14, 2017 - If the series converges for ALL values of x, ? is said to be infinite. How do we EXAMPLE: Find the radius of convergence of the power series. ?. ? n=0. (x + 1) Jan 25, 2016 - In general, a power series converges whenever is close to , and may diverge if is far. B ! B away from . The maximum allowed distance from is called the ! ! radius (2) The power series diverges in the domain |x ? x0|L > 1. (3) The power series may or may not converge at |x ? x0|L = 1. Therefore, if L = 0, then ? = 1 L is the series radius of convergence; if L = 0, then the radius of convergence is ? = ?. The series converges for |x| < 8 and diverges for |x| > 8. The basic facts are these: Every power series has a radius of convergence 0 ?. R ? ?, which depends on the coefficients an. The power series converges A power series may converge for some values of x and may diverge for others. Example In Definition The Radius of convergence (R.O.C.) of the power series. Math 122. Fall 2008. Recitation Handout 17: Radius and Interval of Convergence. Interval of Convergence. The interval of convergence of a power series: cn. x a. Math 122. Fall 2008. Recitation Handout 17: Radius and Interval of Convergence. Interval of Convergence. The interval of convergence of a power series: cn. x a. Mar 23, 2010 -