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Summation Notation?

Hi, can someone please explain what part of mathematics covers an introduction to summation notation. Single sums, double sums, triple sums, laws, solving strategies, divergence and convergence and so on. I would like to learn as much as possible about sums starting at the very basics. Is summation notation introduced in algebra, pre-calculus, calculus? Or somewhere else? Any books you can recommend that explain summation and series well? Thanks.

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  • 3 years ago

    I think there's a chance that you might see summation notation in pre-calculus, although it likely depends on the teacher. It will appear in calculus in the definition of Riemann sums for integrals. Later in the calculus sequence will come a few chapters on convergence and other uses such as Taylor polynomials (power series representations of functions).

    I don't have a definitive textbook suggestion, but I have some online options:

    ~ Use a search engine to look up 'summation notation basics' and/or 'sigma notation'. There will be links to explanatory pages, some of which have a few practice problems and solutions.

    ~ There is a site which I use when I need a quick refresher on calculus topics. It's called 'Paul's Online Math Notes'. The author appears to be a professor at some university (called Lamar University). I like the site because the explanations are clear and good examples are shown. There is also a link to practice problems and solutions for each topic. That's the part which makes it so useful, in my opinion.

    Here's the introduction page to his chapter on sequences and infinite series. Use the 'Next Section' button at the top to see other pages.

    http://tutorial.math.lamar.edu/Classes/CalcII/Seri...

    Other than that, the calculus textbooks by James Stewart are often used. (I have found that the above website actually mirrors the Stewart textbooks pretty closely. The content is not identical, but the topics covered are about the same and in the same order.)

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