Forior series and sequence; Infinite Sequence and Series by BERNHARD W. BACH JR. full Book: Geometric series, Arathematic series, Harmonic Series

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'Infinite Sequence and series' were introduced briefly in a Peview of Calculus in connection with Zeno's paradoxes and the decimal representation of numbers. There importance in Calcuus stems for Newtons's idea of representation function as a sum of infinite series. For insance, in finding areas he often integrated a function by first expression it as a series and then integrating each term of the series. We wil persue an idea in Section 11.10 in oder tointegrate some basic and important exponential functions.

Many of the functions that aries in tha mathematical physics and chemistry, such as Bassel function, are defined as a sum of the series. So it is very important to fimiiar with the basic concepts of convergence of iNFINITE sequence and series.

Physicists also use the series in other way as we see in section 11.11. In studying field of diverse as Optics, Special relaivety, and electromagnitism, they analyze frnomina by a function with the first few terms in the series that represent it.

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Zeeshan Haider

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