MATH 1B Lecture 18: Power Series
Document Summary
Math 1b: calculus - lecture 18: power series. Power series - the sum from n=0 to of cnxn. This is a power series centered at 0. A general power series is a series of the form the sum of n=0 to of cn(x-a)n. We say the power series is centered at a. For a given power series, the sum of x=0 to cn(x-a)n, there are only three possibilities: 3. the series converges when x=a; the series converged for all x; there is a value of r such that the series converges if |x-a|r. We have to be careful with things like (d/dx) (the sum from n=0 to of (xn / n! If the power series the sum from x=0 to of cn(x-a)n has radius of convergence r>0, then the function f is defined by: F(x) = c0 + c1(x-a) + c2(x-a)2 +
