# What is Divergent: Definition and 192 Discussions

The Divergent Series is a feature film trilogy based on the Divergent novels by the American author Veronica Roth. Distributed by Summit Entertainment and Lionsgate Films, the series consists of three science fiction action films set in a dystopian society: Divergent, Insurgent, and Allegiant. They have been produced by Lucy Fisher, Pouya Shabazian, and Douglas Wick.
The series stars Shailene Woodley and Theo James as lead characters Beatrice Prior (Tris) and Tobias Eaton (Four), respectively. The supporting cast includes Ansel Elgort, Zoë Kravitz, and Miles Teller. Kate Winslet played the main antagonist in the first two films. The first film in the series was directed by Neil Burger, while the second and third films were directed by Robert Schwentke.
The Veronica Roth novels consist primarily of the trilogy of Divergent, Insurgent, and Allegiant. Development began in 2011 following Summit's acquisition of the film rights to the Divergent novel in partnership with production company Red Wagon Entertainment. The studios announced production on the sequel following the first film's strong performance in Thursday late-night screenings, where it grossed $4.9 million. They acquired film rights to the Allegiant novel in December 2013, deciding in April 2014 to split the third novel into a two-part film adaptation.The first installment, Divergent (2014), grossed over$288 million worldwide, while the second installment, Insurgent (2015), grossed over $297 million worldwide. Insurgent was also the first Divergent film to be released in IMAX 3D. The third installment, Allegiant (2016), grossed$179 million. Thus, the first three films of the series have grossed over \$765 million worldwide. The series has also experienced declining critical favor with each succeeding film.

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1. ### A How to sum an infinite convergent series that has a term from the end

From my physical problem, I ended up having a sum that looks like the following. S_N(\omega) = \sum_{q = 1}^{N-1} \left(1 - \frac{q}{N}\right) \exp{\left(-\frac{q^2\sigma^2}{2}\right)} \cos{\left(\left(\mu - \omega\right)q\right)} I want to know what is the sum when N \to \infty. Here...
2. ### I Taming a Divergent Series -- But how does it work?

A convergent version ( i.e. convergent in the critical strip) of the traditional series for the Riemann Zeta is derived in the video linked at the bottom. It gives the correct numerical values (at least along the critical line, where I tried it out). But although it works numerically, I'm...
3. ### A Multiplying divergent integrals using Hardy fields approach

I wonder if the following makes sense. Suppose we want to multiply ##\int_0^\infty e^x dx\cdot\int_0^\infty e^x dx##. The partial sums of these improper integrals are ##\int_0^x e^x dx=e^x-1##. Now we multiply the germs at infinity of these partial sums: ##(e^x-1)(e^x-1)=-2 e^x+e^{2 x}+1##...
4. ### Question about boundary layer growth in convergent and divergent ducts

Hi, I was recently reading about convergent-divergent nozzles and was wondering about how boundary layers grow in them. Question: How does a boundary layer grow in a convergent duct in subsonic flow? How does this compare to the growth of a boundary layer in a divergent duct in subsonic flow...
5. ### A What physical meaning can the “determinant” of a divergency have?

I am [working][1] on the algebra of "divergencies", that is, infinite integrals, series and germs. So, I decided to construct something similar to determinant of a matrix of these entities. $$\det w=\exp(\operatorname{reg }\ln w)$$ which is analogous to how determinant of a matrix can be...
6. ### A Why physicists cannot renormalize all divergent integrals?

Why the physicists have troubles with infinities in many physical theories, such as quantum gravity? Why cannot they just use divergent integrals and regularize or renormalize them in the end so to obtain finite values? I mean, operations on divergent integrals are not a problem, and techniques...
7. ### I Divergent series sum, versus integral from -1 to 0

Some popular math videos point out that, for example, the value of -1/12 for the divergent sum 1 + 2 + 3 + 4 ... can be found by integrating n/2(n+1) from -1 to 0. We can easily verify a similar result for the sum of k^2, k^3 and so on. Is there an elementary way to connect this with the more...
8. ### Why does a divergent lens create an interference pattern?

I used a green laser pointer (λ = 532nm). I aimed it at a divergent lens that has a focus of -50cm. The distance from the laser does not play a big role. As a result, a very clear interference pattern with a series of concentric circles appeared on the screen. I did not find a suitable...
9. ### Indirect Proof (open) Divergent series of inverse primes

Show by contradiction that $$\sum_{p\in \mathbb{P}}\dfrac{1}{p} =\sum_{p\;\text{prime}}\dfrac{1}{p}$$ diverges. Which famous result is an immediate corollary?
10. ### Divergent nozzle for releasing pressurised gas

I have air/gas pressurised gas (pressure is 7 barG). I want to know what are the parameters of the divergent nozzle needed so that the pressurised gas can be released to atmospheric pressure level smoothly and necessary enthalpy conversion can be achieved i.e. the air/gas will accelerate to its...
11. ### A Algebra of divergent integrals

Hello, guys! I would like to know your opinion and discuss this extension of real numbers: https://mathoverflow.net/questions/115743/an-algebra-of-integrals/342651#342651 In essence, it extends real numbers with entities that correspond to divergent integrals and series. By adding the rules...

13. ### Why the series is divergent based on the Preliminary test

Interestingly, If I neglect the ##(-1)^n## or ##(-1)^{n+1}## then apply preliminary test, I could find the limit. Whether the limit is not equal to zero, as in series number 1 and 2, then I can conclude the series is divergent. But, if the limit is equal to zero, as in series number 3, then I...

40. ### Infinite series of tan(1/n)

Question ∞ ∑ tan(1/n) n = 1 Does the infinite series diverge or converge? Equations If limn → ∞ ≠ 0 then the series is divergent Attempt I tried using the limit test with sin(1/n)/cos(1/n) as n approaches infinity which I solved as sin(0)/cos(0) = 0/1 = 0 This does not rule out anything and I...
41. ### Magnetostatics: What if "steady" currents were divergent?

Why must steady currents be non-divergent in magnetostatics? Based on an article by Kirk T. McDonald (http://www.physics.princeton.edu/~mcdonald/examples/current.pdf), it appears that the answer is that by extrapolating the linear time dependence of the charge density from a constant divergence...
42. ### B Integral test and its conclusion

I'm really confused about this test. Suppose we let f(n)=an and f(x) follows all the conditions. When you take the integral of f(x) and gives you some value. What are you supposed to conclude from this value?
43. ### Determining Cauchy principal value of divergent integrals

Homework Statement So I've found a ton of examples that show you how to find cauchy principal values of convergent integrals because it is just equal to the value of that integral and you prove that the semi-circle contribution goes to zero. However, I need to find some Cauchy principal values...

pls can u say something on coevolution convergent and divergent evolution and adaptive radiation
45. ### Why is the integral of 1/x from -1 to 1 divergent?

Hey guys, could someone help explain to me why the integral of 1/x from -1 to 1 is considered divergent? It would seem as if the area underneath the function cancels out with each other to give you the result of zero, but apparently this is not the case. Thanks!
46. ### MHB I just want to know one divergent formula

Hello. I asked my professor and he couldn't figure it out. If train A and B leave the same point at the same time, A traveling 60mph, B traveling 75mph, how long will it take for B to have traveled twice as far as A?
47. ### This hypothesis is right about operators on convergent and divergent series?

Sorry for the bad English , do not speak the language very well. I posted this to know if the statement or " hypothesis " is correct . thank you very much =D. First Image:https://gyazo.com/7248311481c1273491db7d3608a5c48e Second Image:https://gyazo.com/d8fc52d0c99e0094a6a6fa7d0e5273b6 Third...
48. ### Is this sequence divergent or convergent?

Homework Statement I'm trying to find out whether or not this sequence diverges or converges. If it converges, then what's the limit. {4+sin(1/2*pi*n)} The Attempt at a Solution This one is a bit confusing to me since sin oscillates between 1 and -1. So if you plug in (pi*infinity)/2, that...
49. ### Convergence of Divergent Series

Consider the two divergent series: $$\sum_{n=k}^{\infty} a_n$$ $$\sum_{n=k}^{\infty} b_n$$ Is it possible for ##\sum_{n=k}^{\infty} (a_n \pm b_n)## to converge?
50. ### Showing harmonic series is divergent

Homework Statement Homework Equations Where do the terms 1/4 come from? Are they ambiguous? The Attempt at a Solution Trying to understand the text[/B]