MHB Unpacking the Master Theorem: Understanding its Proof and Cases

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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
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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)
 

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