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Sequences
  • Basic Concepts of Sequences
  • Arithmetic Sequence
    • Definition of Arithmetic Sequences
    • General Term Formula of Arithmetic Sequences
    • Sum of the First n Terms of Arithmetic Sequences
    • Properties of Arithmetic Sequences
  • Geometric Sequence
    • Definition of Geometric Sequences
    • General Term Formula of Geometric Sequences
    • Sum of the First n Terms of Geometric Sequences
    • Properties of Geometric Sequences
  • Summation of Sequences
    • The Telescoping Method
    • The Grouping Summation Method
    • The Reverse Order Addition Method
    • The Dislocation Subtraction Method
  • Mathematical Induction
    • The Principle of Mathematical Induction
    • Proving Equalities
    • Proving Inequalities
    • Proving Divisibility
  • Recurrence Relations of Sequences
    • The Type aₙ₊₁ = aₙ + d
    • The Type aₙ₊₁ = qaₙ
    • The Type aₙ₊₁ = qaₙ + d
    • The Type aₙ₊₁ = aₙ + f(n)
  • Limits of Sequences
    • The Definition of Limits
    • Properties of Limits
    • Operations on Limits
    • Convergence Criteria
  • Applications of Sequences
    • Compound Interest
    • Loan Repayment
    • Population Growth
    • Geometric Problems
  • Comprehensive Exercises
    • Basic Exercises
    • Intermediate Exercises
    • Advanced Exercises
Sequences
  • Basic Concepts of Sequences
  • Arithmetic Sequence
    • Definition of Arithmetic Sequences
    • General Term Formula of Arithmetic Sequences
    • Sum of the First n Terms of Arithmetic Sequences
    • Properties of Arithmetic Sequences
  • Geometric Sequence
    • Definition of Geometric Sequences
    • General Term Formula of Geometric Sequences
    • Sum of the First n Terms of Geometric Sequences
    • Properties of Geometric Sequences
  • Summation of Sequences
    • The Telescoping Method
    • The Grouping Summation Method
    • The Reverse Order Addition Method
    • The Dislocation Subtraction Method
  • Mathematical Induction
    • The Principle of Mathematical Induction
    • Proving Equalities
    • Proving Inequalities
    • Proving Divisibility
  • Recurrence Relations of Sequences
    • The Type aₙ₊₁ = aₙ + d
    • The Type aₙ₊₁ = qaₙ
    • The Type aₙ₊₁ = qaₙ + d
    • The Type aₙ₊₁ = aₙ + f(n)
  • Limits of Sequences
    • The Definition of Limits
    • Properties of Limits
    • Operations on Limits
    • Convergence Criteria
  • Applications of Sequences
    • Compound Interest
    • Loan Repayment
    • Population Growth
    • Geometric Problems
  • Comprehensive Exercises
    • Basic Exercises
    • Intermediate Exercises
    • Advanced Exercises
This is a beta course, so its structure, chapters, and examples may continue to change.

Applications of Sequences

Sequences are not only an important part of mathematical theory, but also have wide applications in real life. From financial investment to population forecasting, from geometric problems to engineering calculations, sequences are everywhere.

Chapters

  • Compound Interest
  • Loan Repayment
  • Population Growth
  • Geometric Problems
Previous
Convergence Criteria
Next
Compound Interest

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