Precalculus

10.

Sequences, Series, and Mathematical Induction

10.1.

10.1.1.

Definition of Sequence

10.1.2.

Terms of a Sequence

10.1.3.

Finite and Infinite Sequences

10.1.4.

Recursive Formulas

10.1.5.

Explicit Formulas

10.1.6.

Finding Terms of Sequences

10.2.

Arithmetic Sequences

10.2.1.

Definition and Common Difference

10.2.2.

General Term Formula

10.2.3.

Finding Specific Terms

10.2.4.

Finding Common Difference

10.3.

Geometric Sequences

10.3.1.

Definition and Common Ratio

10.3.2.

General Term Formula

10.3.3.

Finding Specific Terms

10.3.4.

Finding Common Ratio

10.4.

Series and Summation Notation

10.4.1.

Definition of Series

10.4.2.

Summation (Sigma) Notation

10.4.2.1.

Index of Summation

10.4.2.2.

Lower and Upper Limits

10.4.3.

Properties of Summation

10.4.4.

Factorial Notation

10.5.

Arithmetic Series

10.5.1.

Sum of Finite Arithmetic Series

10.5.2.

Formula Derivation

10.6.

Geometric Series

10.6.1.

Sum of Finite Geometric Series

10.6.2.

Sum of Infinite Geometric Series

10.6.2.1.

Convergence Condition

10.6.2.2.

Formula for Convergent Series

10.6.3.

10.6.3.1.

10.6.3.2.

Repeating Decimals

10.7.

The Binomial Theorem

10.7.1.

Binomial Coefficients

10.7.1.1.

Combination Notation

10.7.1.2.

Pascal's Triangle

10.7.2.

Binomial Expansion

10.7.3.

General Term in Binomial Expansion

10.7.4.

Applications of Binomial Theorem

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11. Introduction to Limits and Continuity