# Real analysis via sequences and series pdf

## Real Analysis via Sequences and Series | SpringerLink

In mathematics , a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. Series are used in most areas of mathematics, even for studying finite structures such as in combinatorics , through generating functions. In addition to their ubiquity in mathematics, infinite series are also widely used in other quantitative disciplines such as physics , computer science , statistics and finance. For a long time, the idea that such a potentially infinite summation could produce a finite result was considered paradoxical. This paradox was resolved using the concept of a limit during the 19th century. Zeno's paradox of Achilles and the tortoise illustrates this counterintuitive property of infinite sums: Achilles runs after a tortoise, but when he reaches the position of the tortoise at the beginning of the race, the tortoise has reached a second position; when he reaches this second position, the tortoise is at a third position, and so on. Zeno concluded that Achilles could never reach the tortoise, and thus that movement does not exist.## Real Analysis via Sequences and Series

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This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisti Phrase Searching You can use double quotes to search for a series of words in a particular order. Wildcard Searching If you want to search for multiple variations of a word, you can substitute a special symbol called a "wildcard" for one or more letters. You can use? Advanced Searching Our Advanced Search tool lets you easily search multiple fields at the same time and combine terms in complex ways.

Real Analysis via Sequences and Series. Authors; (view affiliations) Limits of Functions. Charles H. C. Little, Kee L. Teo, Bruce van Brunt. Pages PDF .

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Undergraduate Texts in Mathematics are generally aimed at third- and fourth- year undergraduate mathematics students at North American universities.