MATH 2B Chapter Notes - Chapter 11.8: Isaac Newton, Ratio Test, Absolute Convergence

• School: UC-Irvine
• Department: Mathematics
• Course: MATH 2B
• Professor: George Donaldson

Document Summary

Power series are essentially polynomials of in nite degree. For example, recall that the geometric series . We could imagine the series as a function of the variable x = r and write n=0 rn converges to 1. 1 x n=0 xn = 1 + x + x2 + x3 + x4 + . Given that the series converges if and only if 1 < x < 1, we say that the power series/in nite polynomial represents the function 1. Power series have many of the advantages of polynomials in that they are easy to add and to differ- entiate/integrate. The history of power series is long: in the days before concepts such as sine and cosine were thought of as functions, issac newton did much of his work using power series. The delicate issues of convergence were ironed out some decades after newton"s time.