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Prologue to Binomial Theorem (Arrangements)

Basic Binomial Expansions

Binomial Expansion: Simple Examples

Binomial Theorem & Pascal’s Triangle

Binomial Theorem: Introductory Exercises

Tricky Permutations & Combinations Question

Proving Binomial Identities

Finite Series w/ Binomial Coefficients: Substitution

Finite Series w/ Binomial Coefficients: Differentiation

Finite Series w/ Binomial Coefficients: Integration (1 of 2)

Finite Series w/ Binomial Coefficients: Integration (2 of 2)

Binomial Identities: Pascal Example

Greatest Coefficient in Binomial Expansion

Evaluating Specific Binomial Coefficients

Evaluating Coefficients From Two Expansions

Proving Binomial Identities: Comparing Coefficients

Probability Question: With & Without Binomial

Pascal’s Identity (1 of 2)

Pascal’s Identity (2 of 2)

Expressing Terms in a Generalised Binomial Expansion

The Properties of Pascal’s Triangle in nCr Notation

Introduction to nCr Notation

How are Binomial Coefficients related to Pascal’s Triangle?

The Weirdness of Pascal’s Triangle

An ingenious & unexpected proof of the Binomial Theorem (1 of 2: Prologue)

An ingenious & unexpected proof of the Binomial Theorem (2 of 2: Proof)

Demonstrating the Binomial Theorem from Pascal’s Triangle

Sierpinski’s Triangle

Factorials

Determining & Calculating the Greatest Term (example question)

Finding & Evaluating the Greatest Coefficient (example question)

Relating Consecutive Coefficients (and finding the greatest one)

What is the Greatest Coefficient (and why do we care about it)?

Binomial Identity with Even Coefficients Only?

Binomial / Permutations & Combinations Proof (1 of 2)

Binomial / Permutations & Combinations Proof (2 of 2)

Recognising & Substituting Part of a Binomial Expansion

Simplifying Products w/ Factorial Notation

What power of 2 is a factor of “100!”?

Identifying the Constant Term in a Binomial Expansion

Expanding Binomials Involving Substitution

Separating Rational & Irrational Components in Binomial Expansion

Stating the Binomial Theorem w/ Factorial Notation

Developing the Binomial Theorem w/ Pascal’s Triangle

Introduction to Factorial Notation (1 of 2: Why use “!”?)

Introduction to Factorial Notation (2 of 2: How to simplify factorial terms)

Shorthand Notation for nCr

Approximating a Decimal Expansion with Binomial Theorem

Why do all rows of Pascal’s triangle add to powers of 2?

Sigma Notation & Properties of Pascal’s Triangle

nCr Notation

Why Notation & Terminology Are Awesome

Binomial Expansions – Simple Example

Binomial Coefficients & Pascal’s Triangle

Evaluating Specific Binomial Coefficients (Exam Questions)

Summing Binomial Coefficients (Exam Question)

Binomial Coefficients Proof Question

**Prologue to Binomial Theorem (Arrangements) **

**Binomial Expansion: Simple Examples **

**Binomial Theorem & Pascal’s Triangle **

**Binomial Theorem: Introductory Exercises **

**Tricky Permutations & Combinations Question **

**Finite Series w/ Binomial Coefficients: Substitution **

**Finite Series w/ Binomial Coefficients: Differentiation **

**Finite Series w/ Binomial Coefficients: Integration (1 of 2) **

**Finite Series w/ Binomial Coefficients: Integration (2 of 2) **

**Binomial Identities: Pascal Example **

**Greatest Coefficient in Binomial Expansion **

**Evaluating Specific Binomial Coefficients **

**Evaluating Coefficients From Two Expansions **

**Proving Binomial Identities: Comparing Coefficients **

**Probability Question: With & Without Binomial **

**Expressing Terms in a Generalised Binomial Expansion **

**The Properties of Pascal’s Triangle in nCr Notation **

**How are Binomial Coefficients related to Pascal’s Triangle? **

**The Weirdness of Pascal’s Triangle **

**An ingenious & unexpected proof of the Binomial Theorem (1 of 2: Prologue) **

**An ingenious & unexpected proof of the Binomial Theorem (2 of 2: Proof) **

**Demonstrating the Binomial Theorem from Pascal’s Triangle **

**Determining & Calculating the Greatest Term (example question) **

**Finding & Evaluating the Greatest Coefficient (example question) **

**Relating Consecutive Coefficients (and finding the greatest one) **

**What is the Greatest Coefficient (and why do we care about it)? **

**Binomial Identity with Even Coefficients Only? **

**Binomial / Permutations & Combinations Proof (1 of 2) **

**Binomial / Permutations & Combinations Proof (2 of 2) **

**Recognising & Substituting Part of a Binomial Expansion **

**Simplifying Products w/ Factorial Notation **

**What power of 2 is a factor of “100!”? **

**Identifying the Constant Term in a Binomial Expansion **

**Expanding Binomials Involving Substitution **

**Separating Rational & Irrational Components in Binomial Expansion **

**Stating the Binomial Theorem w/ Factorial Notation **

**Developing the Binomial Theorem w/ Pascal’s Triangle **

**Introduction to Factorial Notation (1 of 2: Why use “!”?) **

**Introduction to Factorial Notation (2 of 2: How to simplify factorial terms) **

**Approximating a Decimal Expansion with Binomial Theorem **

**Why do all rows of Pascal’s triangle add to powers of 2? **

**Sigma Notation & Properties of Pascal’s Triangle **

**Why Notation & Terminology Are Awesome **

**Binomial Expansions – Simple Example **

**Binomial Coefficients & Pascal’s Triangle **

**Evaluating Specific Binomial Coefficients (Exam Questions) **

**Summing Binomial Coefficients (Exam Question) **

**Binomial Coefficients Proof Question **

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