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. tworitdash

    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. S

    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

    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. M

    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

    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

    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. S

    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. qnt200

    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. fresh_42

    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. T

    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

    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...
  12. agnimusayoti

    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...
  13. D

    Calculating Divergent Amplitude in Phi-4 Theory

    For the diagram In scalar field theory, I have obtained an integral which looks like $$\int_{0}^{\Lambda} \frac{d^4 q}{(2\pi)^4} \frac{i}{q^2 - m^2 + i\varepsilon} \frac{i}{(p - q)^2 - m^2 + i\varepsilon}$$ I am required to calculate this and obtain the divergent amplitude $$i\mathcal{M} =...
  14. S

    I Assigning a value for integrating a divergent oscillatory function to infinity

    There are meaningful ways to assign values to things like 1 - 1 + 1 + ... or 1 - 2 + 3 - 4 + ... In a similar spirit, is it possible to assign a value to the integral of a function like this: ##f(x)=x*sin(x)## or this one: ##g(x)=Re(x^{1+5i})## (Integrals from some value, say zero, up...
  15. H

    I Divergent vacuum uncertainty of fields in QFT, how to resolve?

    If you calculate the uncertainty of a scalar field in the vacuum state, i.e. ##\langle0\left| \phi^2\right|0\rangle##, you get a divergent integral that comes out to something like $$\frac{1}{4\pi^2}\int_0^\Lambda \frac{k^2 dk}{\sqrt{{m^2}+{k^2}}}$$ Where ##\Lambda## is some momentum cutoff...
  16. bhobba

    I Summing Divergent Series and Borel Summation

    I have recently been investigating summing divergent series and zeta function regularization's relation to dimensional re-normalization. Making some progress, but it is a bit slow despite literature being available...
  17. Ramtin123

    A Computing amplitude for divergent loop diagrams?

    I am trying to compute the cross-section for the diagram below with a divergent triangle loop: where ##X^0## and ##X^-## are some fermions with zero and negative charge respectively. I am interested in low energy limits, so you can consider W-propagator as ##\frac {i\eta_{\mu\nu}} {M_w^2}##...
  18. bhobba

    A Ramanujan Summation and ways to sum ordinarily divergent series

    Hi All Been investigating lately ways to sum ordinarily divergent series. Looked into Cesaro and Abel summation, but since if a series is Abel Mable it is also Cesaro sumable, but no, conversely,haven't worried about Cesaro Summation. Noticed Abel summation is really a regularization...
  19. isukatphysics69

    How to prove that (n+1)/2^n is divergent

    Homework Statement Prove that (n+1)!/2^n is divergent Homework EquationsThe Attempt at a Solution i know that factorials grow faster than exponentials. But on an exam i would not know how to actually prove that this is divergent other than saying that the numerator is growing much faster than...
  20. isukatphysics69

    I Gabriel's Horn and Sum of Infinite Fractions: Contradiction or Connection?

    I don't understand something, the sum n=1 until infinity of (1/n) is a divergent harmonic series meaning that its sum is infinite right? After reading that i started thinking about the finite volume of the function (1/x) being revolved around the x-axis referred to as "Gabriels horn". They say...
  21. F

    Determine whether the series is convergent or divergent

    Homework Statement Homework Equations - The Attempt at a Solution Here's my work : However , the correct answer is : Can anyone tell me where's my mistake ?
  22. V

    Show that a series is divergent

    Homework Statement Show that $$\frac{(-1)^nn!}{z^n}$$ is divergent. Homework Equations We can use the ratio test, which states that if, $$\lim_{n\to\infty}\bigg|\frac{a_{n+1}}{a_n}\bigg|>1$$ a series is divergent. The Attempt at a Solution Applying the ratio test, we find that...
  23. F

    Determine if the improper integral is divergent or not

    Homework Statement Determine if the improper integral is divergent or convergent . Homework Equations - The Attempt at a Solution When i solved the first term using online calculator , the answer was "The integral is divergent" . However , I got 0 . Where is my mistake ?
  24. T

    Is this series divergent or convergent?

    Homework Statement ##\sum_{n=1}^{\infty }1+(-1)^{n+1} i^{2n}## Is this series divergent or convergent? Homework Equations 3. The Attempt at a Solution [/B] I tried using the divergent test by taking the limit as ##n## approaches ##{\infty }##, but both ##i^{2n}## and ##(-1)^{n+1}## will...
  25. D

    I De Sitter Universe: Divergent Parallel Lines?

    The hyperboloid with equation: ## z^2=x^2+y^2-1 ##, embedded in standard 3-D Minkowski space ( +, +, - ) so that ## z^2 ## is negative, has positive Gaussian curvature equal to 1 ( as found directly from its metric: ## ds^2 = \sqrt{ -dτ^2+(Coshτ)^2 dθ^2 } ## induced from the ambient Minkowski...
  26. U

    Determining whether the series is convergent or divergent

    Homework Statement Determine if the series is convergent. Homework Equations ∞ ∑ (((2n^2 + 1)^2)*4^n)/(2(n!)) n=1[/B] The Attempt at a Solution I'n using the Ratio Test and have got as far as (4*(2(n+1)^2+1)^2)/((n+1)((2n^2+1)^2)). I know this series converges but I need to find the...
  27. T

    Divergent Nozzle Homework: Integrating to Get 5

    Homework Statement where the boldface type denotes a vector quantity. In general, the incremental surface dS may be expressed as r dψ R d∅. Examining Figure 1, we see that dS = R2 sin∅ dψ d∅ for this particular nozzle. Substituting Equations 3 and 4 in Equation 2 and integrating ∅ from zero...
  28. B

    Bounded, Divergent Sequence

    Homework Statement Given that ##\{x_n\}## is a bounded, divergent sequence of real numbers, which of the following must be true? (A) ##(x_n)## contains infinitely many convergent subsequences (B) ##(x_n)## contains convergent subsequences with different limits (C) The sequence whose...
  29. G

    A Divergent Diagrams in the Standard Model

    It is my understanding that the task of enumerating all of the divergent diagrams in a quantum field theory can be reduced to analyzing a hand full of diagrams (well, at the moment I know that this is at least true for QED and phi^4 theory), and that all other divergent diagrams are divergent...
  30. Twigg

    Momentum density in a Divergent Beam

    For a divergent paraxial field like $$E = E_0 e^{-\frac{r^{2}}{w(z)^{2}}} e^{-i(kz - tan^{-1}(\frac{z}{z_{0}}))}$$ What is the direction of the momentum density of the E-field. I have two competing feelings about it. 1) The momentum density should be parallel to the Poynting vector, and since...
  31. G

    I Divergent Sums of Linearly Independent Elements

    Suppose we had an infinite series - z = ∑i = 1 to ∞ ( α1(i)x1 + α2(i)x2 + . . . + αm(i)xm ) - rewritten as the cumulative sequence - z(n) = α1(n)x1 + α2(n)x2 + . . . + αm(n)xm - where the xj are linearly independent and normalized (and serve as a finite basis across the sequence). If all...
  32. C

    Is the equivalent lens of two such that f_1+f_2<h divergent?

    The focal of the lens equivalent of two thin lens at distance h is $$1/f=1/f_1+1/f_2+h/(f_1 f_2)$$ Therefore, supposing that ##f_1>0## and ##f_2>0## (both lenses are convergent), if ##f_1+f_2 <h## then the equivalent lens should be divergent. Nevertheless consider the example in picture...
  33. K

    Series problems convergent or divergent

    Poster warned that the homework template is not optional. Determine if they are convergent or divergent, If it converges find the sum: ∞ ∑ 3^(n-1) 2^n n=1 ∞ ∑ ln(1/n) n=1 ∞ ∑ tan^n ( π/6) n=1 I tried to find information on how to solve them but I couldn't, thanks for the help
  34. jlmccart03

    Series: Determine if they are convergent or divergent

    Homework Statement I have a couple of series where I need to find out if they are convergent (absolute/conditional) or divergent. Σ(n3/3n Σk(2/3)k Σ√n/1+n2 Σ(-1)n+1*n/n^2+9 Homework Equations Comparison Test Ratio Test Alternating Series Test Divergence Test, etc The Attempt at a...
  35. T

    MHB Divergent or Convergent Integral

    I have: $$\int_{1}^{2} \frac{1}{x lnx} \,dx$$ I can set $u = lnx$, therefore $du = \frac{1}{x} dx$ and $xdu = dx$. Plug that into the original equation: $$\int_{1}^{2} \frac{x}{x u} \,du$$ Or $$\int_{1}^{2} \frac{1}{ u} \,du$$ Therefore: $ln |u | + C$ and $ln |lnx | + C$ So I need to...
  36. B

    Radius of Convergence for Ratio Test in Calculus Questions

    Homework Statement Homework Equations Ratio test. The Attempt at a Solution [/B] I guess I'm now uncertain how to check my interval of convergence (whether the interval contains -2 and 2)...I've been having troubles with this in all of the problems given to me. Do I substitute -2 back...
  37. B

    Absolutely Convergent, Conditionally Convergent, or Divergent?

    Homework Statement ∞ Σ (-1)n-1 n/n2 +4 n=1 Homework Equations lim |an+1/an| = L n→∞ bn+1≤bn lim bn = 0 n→∞ The Attempt at a Solution So I tried multiple things while attempting this solution and got inconsistent answers so I am thoroughly confused. My work is on the attached photo. I found that...
  38. T

    MHB Divergent Or Convergent Series

    I have this: $$ \sum_{n = 1}^{\infty} \frac{n^n}{3^{1 + 3n}}$$ And I need to determine if it is convergent or divergent. I try the limit comparison test against: $$ \frac{1}{3^{1 + 3n}}$$. So I need to determine $$ \lim_{{n}\to{\infty}} \frac{3^{1 + 3n} \cdot n^n}{3^{1 + 3n}}$$ Or $$...
  39. Kaura

    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...
  40. P

    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...
  41. T

    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?
  42. saybrook1

    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...
  43. Kay Nanny Jay

    Coevolution, Convergent & Divergent Evolution, Adaptive Radiation

    pls can u say something on coevolution convergent and divergent evolution and adaptive radiation
  44. ecoo

    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!
  45. J

    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?

    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...
  47. S

    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...
  48. P

    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?
  49. B

    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]