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# 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.
• 9.E: Sequences and the Binomial Theorem (Exercises)
These are homework exercises to accompany Chapter 9 of Stitz and Zeager's "Pre-Calculus" Textmap.

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.

### Contributors

• Carl Stitz, Ph.D. (Lakeland Community College) and Jeff Zeager, Ph.D. (Lorain County Community College)