Public learning track
Geometric Sequences, Series, and Infinite Convergence
11th Grade · Math · Open Global Math
8 lessons
Goal
Analyze geometric progressions, evaluate partial sums using sigma notation, and determine convergence and infinite sums for |r| < 1.
Featured Diagrams
Geometric Sequences: Explicit and Recursive Definitions
8 lessons
0 of 8 done
- 1Geometric Sequences: Explicit and Recursive DefinitionsUp nextStart
- 2Finding Terms and Common Ratios in Geometric SequencesPremiumNot started yet
- 3Geometric Means and Sequence InterpolationNot started yet
- 4Finite Geometric Series Formula and Partial SumsNot started yet
- 5Finding Sums of Geometric Series in Sigma NotationNot started yet
- 6Infinite Geometric Series: Convergence and Sum to InfinityNot started yet
- 7Converting Repeating Decimals Using Infinite Geometric SeriesNot started yet
- 8Applications of Geometric Series in Finance and FractalsNot started yet
Curriculum Framework
11th Grade · Math · Open Global Math
1
6 lessons
Advanced Function Foundations, Domain Analysis, and Notation
Master the formal mapping definition of functions, algebraic and contextual domain-range analysis, and advanced function notation.
2
8 lessons
Comprehensive Analysis of Function Graphs and Key Features
Analyze, interpret, and sketch critical graph features across diverse function families including extrema, behavior, and symmetry.
3
6 lessons
Piecewise, Step, and Modulus Functions
Analyze, evaluate, and sketch piecewise-defined, greatest integer (floor/ceiling), and absolute value (modulus) functions.
4
6 lessons
Function Operations and Advanced Composition
Perform algebraic arithmetic on functions, construct composite functions, and evaluate nested domains.
5
7 lessons
Inverse Functions, Invertibility, and Domain Restrictions
Determine invertibility, construct inverses algebraically and graphically, restrict domains, and verify inverse relationships via composition.
6
7 lessons
Geometric Transformations of General Functions
Apply single and multi-step vertical and horizontal translations, stretches, compressions, and reflections to arbitrary functions y = f(x).
7
6 lessons
Arithmetic Sequences, Recursive Definitions, and Series
Analyze arithmetic progressions explicitly and recursively, compute nth terms, and evaluate arithmetic series in sigma notation.
8
8 lessons
Geometric Sequences, Series, and Infinite Convergence
Analyze geometric progressions, evaluate partial sums using sigma notation, and determine convergence and infinite sums for |r| < 1.