Public learning track
The General Binomial Theorem and Power Approximations
12th Grade · Math · Open Global Math
6 lessons
Goal
Expand binomial expressions for positive integers and generalize to rational exponents with convergence criteria to approximate numerical and functional values.
Featured Diagrams
Binomial Expansions for Positive Integers and Combinatorics
6 lessons
0 of 6 done
- 1Binomial Expansions for Positive Integers and CombinatoricsUp nextStart
- 2Finding Specific Terms and Coefficients in Binomial ExpansionsPremiumNot started yet
- 3The Extended Binomial Theorem for Rational ExponentsNot started yet
- 4Expanding General Binomials with Rational PowersNot started yet
- 5Validity Intervals and Convergence Criteria for Binomial SeriesNot started yet
- 6Numerical and Functional Approximations Using Binomial SeriesNot started yet
Curriculum Framework
12th Grade · Math · Open Global Math
1
6 lessons
Real Number Systems, Density, and Completeness
Analyze decimal and non-decimal representations of real numbers, prove irrationality, and demonstrate the structural density and completeness properties of number systems.
2
5 lessons
Advanced Radicals, Polynomial Division, and Algebraic Fractions
Manipulate algebraic expressions with rational exponents and surds, apply polynomial division and theorems, and simplify complex algebraic fractions.
3
5 lessons
Partial Fraction Decomposition Techniques
Decompose proper and improper rational functions into partial fractions with linear and repeated linear denominator factors.
4
6 lessons
The General Binomial Theorem and Power Approximations
Expand binomial expressions for positive integers and generalize to rational exponents with convergence criteria to approximate numerical and functional values.
5
7 lessons
Sequences, Recurrence Relations, and Series Convergence
Analyze explicit and recursive sequences, evaluate finite and infinite series in sigma notation, determine convergence, and model real-world dynamic phenomena.