Series Expansions
Staff posted on October 23, 2006 |
 In the fith century B.C. the theory on the limit of a sequence was introduced by the Greek philosopher Zeno of Elea. By definition, a sequence {an} is a set of real numbers written in a define natural order. For instance, the sequence {1, 1/2, 1/3, 1/4,...} can be described by a formula for nth term {1, 1/2, 1/3, 1/4,...}  is called the range of the sequence A sequence {an} has the limit L and is written,   A series is formed by many terms (maybe infinitely many) added together. This is the basic difference between series and sequences. An infinite series(or simply a series) is denoted The Geometric Series The geometric series, is convergent if | r | < 1 and its sum is  The Alternating Series satifies Then, the series is convergent. Alternating series estimation theorem   The Root and Ratio Tests The Ratio Test The Root Test Power Series Taylor and Maclaurin Series    Important Maclaurin series and there intervals of convergence:          The Binomial Series  Recommended For You