MATH201 Lecture Notes - Lecture 21: Ansatz, Taylor Series, Absolute Convergence
18 Jun 2015
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Math 201 lecture 23: power series method for equations with poly- nomial coefficients. 07, 2012: many examples here are taken from the textbook. The rst number in () refers to the problem number in the ua custom edition, the second number in () refers to the problem number in the 8th edition: radius of convergence, theoretical issues. Theorem 1. (radius of convergence) for any power series p an (x x0)n, there is a number. This particular number is called the radius of convergence. In other words, for any |x x0| < , the in nite sum of numbers (1) (2) X an (x x0)n n(cid:17) (cid:12)(cid:12)(cid:12)(cid:12) lim indeed equals a number, while for any |x x0| > the in nite sum is either in nity or does not have a limit at all. Consequently, inside |x x0| < , the power series indeed represent a well-de ned function: how to calculate radius of convergence.
