9: Sequences and the Binomial Theorem

Precalculus · LibreTexts

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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 \(\displaystyle f(x)=1/x\) and the \(\displaystyle x\)-axis for \(\displaystyle x≥1\). 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.

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