/sci/ - Science & Math

>>11000887
Oh btw, I thought about it more, and you can quickly show it's not infinity-infinity.
The sums are bounded, the first one by say 2n, or even closer by (2n)^(1-(1/a)), so though it may diverge, it's not infinity.

>>11001713
>>11001749
You're not plugging the 0 into the ratio at that point, and the sums take whatever value they take, it could be 0/0, but most of the time it's not. It's the ratio though that must hold through the system.
So I guess you think l'hopitals rule is broken also?

>>11002134
They don't need to converge because they are bound and not infinite, even if divergent, and the proof isn't necessitated on their convergence-divergence anyways, but on the symbolic relations of the sums and coefficients.

>>10150541
Here's an example of a technique I developed for operational calculus. It lets you remove the discontinuities in piecewise functions, and create 1 analytic function from the pieces. This is the resolution of a 3 piecewise function into 1 to create a plateau function.