Chapter 8: Sequences, Series, Induction, and Probability
In mathematics you don’t understand things. You just get used to them.
Why This Matters
Sequences and series are mathematics in motion — patterns that unfold step by step.
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Fibonacci found his sequence in rabbit populations
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Pascal found his triangle in combinations
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Compound interest is a geometric series
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The digits of \(\pi\) form an infinite sequence we’re still computing
Probability is the mathematics of uncertainty — essential in a world where nothing is certain.
Sections
| Section | Topic | Key Skill | Status |
|---|---|---|---|
Sequences and Series |
Notation, summation |
[ ] Not Started |
|
Arithmetic Sequences and Series |
\(a_n = a_1 + (n-1)d\) |
[ ] Not Started |
|
Geometric Sequences and Series |
\(a_n = a_1 \cdot r^{n-1}\) |
[ ] Not Started |
|
Mathematical Induction |
Prove for all \(n\) |
[ ] Not Started |
|
Binomial Theorem |
Expand \((a+b)^n\) |
[ ] Not Started |
|
Counting Principles |
Permutations, combinations |
[ ] Not Started |
|
Introduction to Probability |
\(P(E) = \frac{n(E)}{n(S)}\) |
[ ] Not Started |