MATH-M 212 Lecture Notes - Lecture 20: Alternating Series
Document Summary
Theorem 9. 22- the form of a convergent power series: if is represented by a power series for all in open interval containing , then and: o. Definition of taylor and maclaurin series: if a function has derivatives of all orders at , then the series is called the taylor. Series for at: if , series is the maclaurin series for : Theorem 9. 23- convergence of taylor series (not taught: if for all in the interval , then the taylor series for converges and equals. Derive the power series for centered at 1 and find its interval of convergence. o o o o: assemble series, find interval: Derive the power series for and find its interval of convergence. Ex: we know, we know the power series of, can substitute in , interval: always nonnegative. Derive the power series for centered at 0. Ex. o o o o o: series:
