Series Expansions
The Engineer posted on October 23, 2006 | 11462 views
 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
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