MATH128 Study Guide - Ratio Test
Document Summary
Cn (x a)n: when a = 0 x is a variable cn is coefficient of nth term. Cn xn form: n=0 called maclaurin series. Interval of convergence: (a r, a + r) Functions as power series: power series model data, simplify messy functions to simpler polynomials, Cn (x a)n has radius of convergence r > 0, Cn (x a)n is differentiable (and so continuous) and. If the power series n=0 then f(x) = n=0 integrable on the interval (a r, a + r). radii of convergence for these new functions remain r. However, convergence at the endpoints of the interval may change. Example: n=0 power series representations for 1/(1 x) , ln(1 x), arctan x.
