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Mathematics LibreTexts

9: Sequences and Series

  • Page ID
    120827
    • Gilbert Strang & Edwin “Jed” Herman
    • OpenStax

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    The topic of infinite series may seem unrelated to differential and integral calculus. In fact, an infinite series whose terms involve powers of a variable is a powerful tool that we can use to express functions as “infinite polynomials.” We can use infinite series to evaluate complicated functions, approximate definite integrals, and create new functions. In addition, infinite series are used to solve differential equations that model physical behavior, from tiny electronic circuits to Earth-orbiting satellites.

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    Thumbnail: For the alternating harmonic series, the odd terms \(S_{2k+1}\) in the sequence of partial sums are decreasing and bounded below. The even terms \(S_{2k}\) are increasing and bounded above.


    This page titled 9: Sequences and Series is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Gilbert Strang & Edwin “Jed” Herman (OpenStax) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.