After 10+ years, I’ve forgotten all the math that I learned in school and never used. Though I don’t think I ever learned about this in particular, reading about it is confusing because the terms used have long since been forgotten, E.G. partial sums, convergence, divergence.. throw a 5 year old a bone please?
In: Mathematics
It’s just an arbitrary number assigned to diverging sums
Diverging means not converging, which in turn basically means growing closer to a certain value.
The easiest example of a convergent sum is 1/2^n from n=0 to Infinity
It’s easy to see that the limit of this sum is 2 by realizing that you’re essentially splitting a 2×1 Rectangle in 2, and then splitting that halfed part again etc. (1+1/2+1/4…)
The sum over n (n=1 to infinity) is divergent, no matter what you try, it will always grow larger than any limit you might set
For divergent sums you can sometimes make up a pseudo-limit like for (-1)^n by weighting the sum of the first x values(=partial sum) with 1/x. In this case the limit would be 1/2. See Wikipedia article for exact formula
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