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1
Prologue to Binomial Theorem (Arrangements)
2
Basic Binomial Expansions
3
Binomial Expansion: Simple Examples
4
Binomial Theorem & Pascal's Triangle
5
Binomial Theorem: Introductory Exercises
6
Tricky Permutations & Combinations Question
7
Proving Binomial Identities
8
Finite Series w/ Binomial Coefficients: Substitution
9
Finite Series w/ Binomial Coefficients: Differentiation
10
Finite Series w/ Binomial Coefficients: Integration (1 of 2)
11
Finite Series w/ Binomial Coefficients: Integration (2 of 2)
12
Binomial Identities: Pascal Example
13
Greatest Coefficient in Binomial Expansion
14
Evaluating Specific Binomial Coefficients
15
Evaluating Coefficients From Two Expansions
16
Proving Binomial Identities: Comparing Coefficients
17
Probability Question: With & Without Binomial
18
Pascal's Identity (1 of 2)
19
Pascal's Identity (2 of 2)
20
Expressing Terms in a Generalised Binomial Expansion
21
The Properties of Pascal's Triangle in nCr Notation
22
Introduction to nCr Notation
23
How are Binomial Coefficients related to Pascal's Triangle?
24
The Weirdness of Pascal's Triangle
25
An ingenious & unexpected proof of the Binomial Theorem (1 of 2: Prologue)
26
An ingenious & unexpected proof of the Binomial Theorem (2 of 2: Proof)
27
Demonstrating the Binomial Theorem from Pascal's Triangle
28
Sierpinski's Triangle
29
Factorials
30
Determining & Calculating the Greatest Term (example question)
31
Finding & Evaluating the Greatest Coefficient (example question)
32
Relating Consecutive Coefficients (and finding the greatest one)
33
What is the Greatest Coefficient (and why do we care about it)?
34
Binomial Identity with Even Coefficients Only?
35
Binomial / Permutations & Combinations Proof (1 of 2)
36
Binomial / Permutations & Combinations Proof (2 of 2)
37
Recognising & Substituting Part of a Binomial Expansion
38
Simplifying Products w/ Factorial Notation
39
What power of 2 is a factor of "100!"?
40
Identifying the Constant Term in a Binomial Expansion
41
Expanding Binomials Involving Substitution
42
Separating Rational & Irrational Components in Binomial Expansion
43
Stating the Binomial Theorem w/ Factorial Notation
44
Developing the Binomial Theorem w/ Pascal's Triangle
45
Introduction to Factorial Notation (1 of 2: Why use "!"?)
46
Introduction to Factorial Notation (2 of 2: How to simplify factorial terms)
47
Shorthand Notation for nCr
48
Approximating a Decimal Expansion with Binomial Theorem
49
Why do all rows of Pascal's triangle add to powers of 2?
50
Sigma Notation & Properties of Pascal's Triangle
51
nCr Notation
52
Why Notation & Terminology Are Awesome, Not Boring
53
Binomial Expansions - Simple Example
54
Binomial Coefficients & Pascal's Triangle
55
Evaluating Specific Binomial Coefficients (Exam Questions)
56
Summing Binomial Coefficients (Exam Question)
57
Binomial Coefficients Proof Question
Description:
Explore the proofs and applications of the Binomial Theorem in this comprehensive 8-hour video playlist. Delve into binomial expansions and their ubiquitous presence in mathematics, from basic algebra to permutations and combinations. Discover the fascinating connection between factorials and Pascal's Triangle, and learn to solve complex problems related to polynomials and probability. Cover topics such as basic binomial expansions, Pascal's Triangle, binomial identities, finite series with binomial coefficients, probability questions, nCr notation, factorial notation, and Sierpinski's Triangle. Work through numerous examples and exam-style questions to reinforce your understanding of this fundamental mathematical concept.

Binomial Theorem

Eddie Woo
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#Mathematics #Algebra #Statistics & Probability #Probability #Combinatorics #Permutations #Pascal's Triangle #Binomial Theorem
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Prologue to Binomial Theorem (Arrangements)