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Mathematics LibreTexts

9: Sequences and the Binomial Theorem

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  • 9.1: Sequences
    In this section, we introduce sequences which are an important class of functions whose domains are the set of natural numbers.
  • 9.2: Summation Notation
    In the previous section, we introduced sequences and now we shall present notation and theorems concerning the sum of terms of a sequence.
  • 9.3: Mathematical Induction
    Here we introduce a method of proof, Mathematical Induction, which allows us to prove many of the formulas we have merely motivated previously.
  • 9.4: The Binomial Theorem
    Simply stated, the Binomial Theorem is a formula for the expansion of quantities for natural numbers.

Thumbnail: The sum of the areas of the rectangles is greater than the area between the curve f(x)=1/x and the x-axis for x1. Since the area bounded by the curve is infinite (as calculated by an improper integral), the sum of the areas of the rectangles is also infinite.


This page titled 9: Sequences and the Binomial Theorem is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by Carl Stitz & Jeff Zeager via source content that was edited to the style and standards of the LibreTexts platform.

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