Uploaded April 2022 | Updated September 2026, 1 week ago
The answer to the question in the title is that it depends on how you define the infinite sum function. Until the infinite sum function is specified, the question is not well-defined; it's the equivalent of asking "what is f(5)?" without defining the function f.
The sum of all natural numbers, and the sums of divergent series more generally, are often debated because it seems incoherent to say that a divergent sum equals a finite number. This video explains the machinery used to obtain finite outputs from divergent infinite series.
Calculus Problems playlist: youtube.com/playlist?list=PLug5ZIRrShJGFne7YhMi-4eYsUKzkITao
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Music: C418 - Pr Department
The answer to the question in the title is that it depends on how you define the infinite sum function. Until the infinite sum function is specified, the question is not well-defined; it's the equivalent of asking "what is f(5)?" without defining the function f.
The sum of all natural numbers, and the sums of divergent series more generally, are often debated because it seems incoherent to say that a divergent sum equals a finite number. This video explains the machinery used to obtain finite outputs from divergent infinite series.
Calculus Problems playlist: youtube.com/playlist?list=PLug5ZIRrShJGFne7YhMi-4eYsUKzkITao
Subscribe to see more new math videos!
Music: C418 - Pr Department
