MHB Unpacking the Master Theorem: Understanding its Proof and Cases

Click For Summary
The discussion centers around proving a specific theorem through an iterative approach. Participants emphasize the need to clarify which cases correspond to different scenarios: when the first term is dominant, when each part of the summation is equally dominant, and when the summation behaves like a geometric series. There is a call for further explanation and justification for these distinctions to strengthen the proof.
evinda
Gold Member
MHB
Messages
3,741
Reaction score
0

Attachments

  • beg.PNG
    beg.PNG
    15.9 KB · Views: 104
  • case1.PNG
    case1.PNG
    5.2 KB · Views: 95
  • case2.PNG
    case2.PNG
    5.6 KB · Views: 87
  • case3.PNG
    case3.PNG
    7.6 KB · Views: 94
Last edited:
Technology news on Phys.org
Now I found the following proof:

View attachment 4435

Don't we have to explain further which case correponds to which of the following cases

  • The first term is dominant.
  • Each part of the summation is equally dominant.
  • The summation is a geometric series

and justify why it is like that? (Thinking)
 

Attachments

  • proof11.PNG
    proof11.PNG
    9.3 KB · Views: 104

Thread 'For those who ask: "What programming language should I learn?"'

Learn If you want to write code for Python Machine learning, AI Statistics/data analysis Scientific research Web application servers Some microcontrollers JavaScript/Node JS/TypeScript Web sites Web application servers C# Games (Unity) Consumer applications (Windows) Business applications C++ Games (Unreal Engine) Operating systems, device drivers Microcontrollers/embedded systems Consumer applications (Linux) Some more tips: Do not learn C++ (or any other dialect of C) as a...
View full post »

Similar threads

B I've been trying to understand the proof for the binomial theorem
  • · Replies 6 ·
Replies
6
Views
2K
Is this computability theory proof correct?
  • · Replies 1 ·
Replies
1
Views
2K
Insights Fermat's Last Theorem
  • · Replies 105 ·
4
Replies
105
Views
7K
I Fundamental theorem of arithmetic from Jordan-Hölder theorem
  • · Replies 5 ·
Replies
5
Views
2K
I On a proof of the converse of the supporting hyperplane theorem
  • · Replies 9 ·
Replies
9
Views
2K
A Question about proof of Great Picard Theorem
  • · Replies 3 ·
Replies
3
Views
3K
I Is an algorithm for a proof required to halt?
  • · Replies 3 ·
Replies
3
Views
2K
I Uniqueness of reduced row echelon form (proof verification)
  • · Replies 4 ·
Replies
4
Views
2K
I Why prove Taylor's theorem with p(x)=q(x)−((b−a)^n/(b−x)^n)q(a)?
  • · Replies 9 ·
Replies
9
Views
3K
Calculus What Is the Best Calculus Book for Self-Learners?
  • · Replies 17 ·
Replies
17
Views
8K