Mit18 330 s12_chapter1

This document provides an introduction to series and sequences. It discusses key concepts such as convergence vs divergence of sequences and series. Specifically, it defines what an infinite sum is, absolute vs conditional convergence, and common tests to determine convergence like the integral test and alternating series test. It also introduces the big-O, little-o, and big-Theta notations used to compare the growth or decay rates of sequences. The overall goal is to establish an understanding of convergence of series before delving into numerical analysis applications that make use of infinite series like Taylor and Fourier series.