LT
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Top Tracks
1
Intro
2
Deriving the Solution
3
The Super Recursive Formula
4
The Recursive Formula
5
Introduction
6
A few Disclaimers
7
Logarithms
8
A minor setback
9
Laying the Background
10
The Bubble Sort Curve
11
How to Take the Factorial of Any Number
12
Mathematically Describing Diagrams
13
History and Conventions
14
How Bubble Sort Works
15
The Miracle
16
Stretching the Diagrams
17
Visual Derivation
18
Symbolic Derivation
19
A Recursive Formula
20
Graphing the Harmonic Numbers
21
Using the Recursive Formula
22
Graphing the Solution
23
A Rigorous Solution
24
Finding the Interval
25
Our Constraints
26
Extending the Harmonic Numbers to the Reals
27
Deriving the Main Formula
28
Flattening Out
29
Notes About This Video
30
Stating the Problem
31
Going to the Right
32
The Forward Difference
33
Background and Notation
34
The First Solution
35
Deriving the Iterated Forward Difference Formula
36
The Second Solution
37
High Order Forward Differences
38
The General Solution
39
Nasty Nested Sums
40
The General Solution, For Real
41
The Sine Product Formula
42
How to Extend the Sum of Any* Function
43
What You Came Here For
44
The Published Solution
45
Factorials, Harmonic Numbers, and Trig
46
The End
47
The True Logarithmic Derivative
48
An Infinite Sum for Cotangent
49
Final Thoughts
50
Comparing the Solutions
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