Power Series

In this video, we answer the question: when do power series converge? We prove that power series either converge only at zero, everywhere, or on some interval centered around zero. We prove that power series converge uniformly on any compact subset of their interval of convergence. We also prove that open intervals of convergence are preserved under term-by-term differentiation or antidifferentiation. We combine this with results from the previous video in some examples.

Sources:

Abbott, Stephen. Understanding Analysis. 2nd ed., Springer, 2015.

Lebl, Jiří. Basic Analysis I: Introduction to Real Analysis, Volume I. Version 5.4, June 8, 2021.

Видео Power Series канала Joel Anderson