MATH 222 Study Guide - Midterm Guide: Partial Fraction Decomposition, Integral Test For Convergence, Taylor Series
Document Summary
First, we need to note the di erence between a sequence and a series. A sequence is an in nitely long list of numbers. 2n for n 0 de nes sequence by describing the nth term. For example an = 1 the sequence a0 = 1, a1 = 1. A series can be de ned for any sequnce by adding up all of the entries in that sequence. We can ask two di erent questions about a sequence: To answer the rst question, we compute limn an. If this limit exists and it is nite then our sequence converges. The second question has a very similar answer, and many people confuse the two. To nd out if our sequence converges, we compute n=0 an. If this limit exists and it is nite then our series con- verges. The second question is actually much harder than the rst.
