# 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)