Often, you’ll want to know whether a series converges (i.e. reaches a certain number) or diverges (does not converge). Figuring this out from scratch can be an extremely difficult task —something that’s beyond the scope of even a calculus II course. Thankfully, mathematicians before you...
To evaluate this equation, first notice that n →∞. The fraction above is equal to 1 which is greater than zero. Since the amount is greater than zero we know that through the limit comparison test that the series converges with a known convergent series. Direct Comparison Test The Dire...
where a step function input is applied as a sudden change in pressure. The measured responses indicate that the system is nonlinear, as it fails the amplitude-scale invariance test. To describe the mass transport through a membrane made of porous materials, the Porous ...
The general experience with batch size is always confusing because there is no single “best” batch size for a given data set and model architecture. If we decide to pick a larger batch size, it will train faster and consume more memory, but it might show lower accuracy in the end. Fir...
Hi there. I have this interesting problem which I don't know how to solve. I'll post it here because I think more people will se it, but I'm not sure if this is the proper subforum. The problem says: How can be sure that ∑n=1∞1nsin(nx) isn't the ...
If you want to see a hologram, you don't have to look much farther than your wallet. But the most impressive holograms are large scale and illuminated with lasers or displayed in a darkened room with carefully directed lighting. Learn how a hologram, lig
In Theorem 4.1, we show that in the supercritical phase, under the assumption that the 2+ϵ moment of the radius of influence random variable is finite for some ϵ>0, the appropriately scaled rightmost vertex in the rumour cluster converges to a deterministic positive constant almost surely....
Demographers might use this tool to evaluate which countries have similar patterns of population growth, both in terms of value and profile of time series. Tool outputs A number of outputs are created by this tool. A 2D feature class showing each location in the Input Space Time Cu...
Well, that's nice to know! We have no idea about Bernoulli numbers, or any other properties of Riemann zeta functions ζ(s)ζ(s), yet we obtained some meaningful result with seemingly completely wrong formal manipulations. So, if we ever want to compute the infinite sum Sk=1k+2k+3k+4k...
Sequence and Series> Not allbounded sequencesconverge, but if a bounded a sequence is alsomonotone(i.e. if it is either increasing or decreasing), then it converges. This fact, that every bounded monotone sequence converges is called themonotone convergence theorem[1]. ...