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. M

    Convergent or Divergent: Is this a Convergent Series?

    Mod note: Moved from a homework section. 1. Homework Statement this is my lecturer's notes, he says it is a divergent series, but this seems like an obvious convergent series to me.. could someone verify? Homework Equations https://www.dropbox.com/s/mc5rth0cgm94reg/incorrect maths.png?dl=0...
  2. A

    MHB Sum of infinite divergent series

    It is well known that the below series are divergent $1 - 1 + 1 - 1 + \cdots $ $1 - 2 + 3 - 4 + \cdots $ $1 + 2 + 3 + \cdots $ But after i watched a video in youtube for the channel " Numberphile " they proved that the first is equal to 1/2 , 1/4 and the last one is -1/12 ! The way to...
  3. titasB

    Divergent Sequence Homework: Determine Convergence

    Homework Statement Determine whether the sequence is convergent or divergent Homework Equations an = {nn / n! } The Attempt at a Solution an = ( n . n. n ... n ) / 1 . 2 . 3 ... n ) ⇒ an =n [ ( n . n. n ... n ) / 1 . 2 . 3 ... n ) ] ⇒ as n → ∞ , an → ∞ This is further confirmed by...
  4. Sinisa

    Where is sum of divergent series used in physics?

    Hello everyone! My question is: Where is sum of divergent series and divergent integrals used in physics? What it all means? Where can I find examples of divergent integrals? Is there a book of problems for physicists? I am mathematician. I developed a method for summing divergent series...
  5. J

    Calculating Mass Flow Rates and Mach Numbers in a Convergent-Divergent Nozzle

    Hi, I hope that, given I've sourced what I can, you may be able to help? I'm Currently working on a lab report for my Aeroengines unit based on Convergent-Divergent nozzle (http://imgur.com/HQML2Au). From the drawing, I have been provided D1, D2, D3, D4, T1, T2, T3, T4, P1, P2, P3, Velocity...
  6. G

    Sequence (n)/(n^n) Convergent or Divergent and Limit?

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  7. U

    Determine if the series is convergent or divergent and radio test

    Homework Statement 1+\dfrac{2^2}{2!}+\dfrac{3^2}{3!}... \infty The Attempt at a Solution t_n = \dfrac{n^2}{n!} \\ \dfrac{n}{(n-1)(n-2)...1} I tried applying the Ratio Test but couldn't find another function which would give me a finite limit when divided by that function.
  8. I

    MHB How to determine whether an integral is convergent or divergent

    Determine whether the integral is convergent or divergent. Evaluate those that are convergent. $\int_{0}^{9} \ \frac{1}{\sqrt[3]{x-1}},dx$ $\int_{-\infty}^{\infty} \ \cos\left({\pi t}\right),dt$ how do i determine whether it's conver/diver?
  9. B

    Series Convergence Test for ∑ 5^n/(4^n +3)

    Homework Statement Which of the series, diverge or converge ∑ 5^n/(4^n +3 ) Homework Equations The Attempt at a Solution Taking the limit as n→∞ we have (5^n ln 5)/ (4^n ln 4) , my question is here how does it become like this, which part am I missing here?
  10. L

    Problem with summing a divergent series

    Hello, The point of this thread is to find the mathematical error in summing divergent series. For example the series: 1+2+4+8+16+32+64+...+... (doubling the numbers, or alternatively: increasing powers of 2). I've seen the argument that you multiply the series by 1, then substitute (2-1)...
  11. S

    MHB Question about determining if the series is convergent or divergent

    Determine if the positive term series is convergent or divergent \sum^{\infty}_{n = 1} \frac{n + cosn}{n^3 + 1} can't I just ignore the cosn and look at it like this: \sum^{\infty}_{n = 1} (-1)^n \frac{n}{n^3 + 1} Then can't I just look at it as n--> \infty and see that I end up with...
  12. A

    Proving Divergence of the Series: \sum_{i=1}^{\infty}\sqrt{n+1}-\sqrt{n}

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  13. G

    Series: Convergent or Divergent?

    Homework Statement Is the following convergent or divergent? ln(2(n+1))-ln(2n) Homework Equations comparison test The Attempt at a Solution I put it into the form ln(1+(1/n)), but I don't understand what to use as Bn for the comparison test. (which is what wolfram alpha uses)
  14. S

    Help with determining if a series is convergent or divergent question

    Homework Statement Problem is attached in this post. Homework Equations Problem is attached in this post. The Attempt at a Solution I know how to find the sum of this series, but I don't know what method to use in order to prove that this series converges. Also I don't understand how I'm...
  15. U

    Series: Divergent or Convergent ?

    How can I tell if the following series is Divergent or Convergent: ∑( e^(6pi*n) sin^2(4pi*n) ) the sum limits are from -infinity to infinity
  16. C

    Divergent or Convergent? Evaluating an Integral with Exponential Function

    Homework Statement Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. ∫ from negative infinity to infinity of (x^8*e^-x^9) The Attempt at a Solution The answer is diverged to infinity. But I got that by guessing. Can someone explain to me why...
  17. S

    Help with proving that Improper Integral is Divergent

    Homework Statement The problem is attached in this post. Homework Equations The problem is attached in this post. The Attempt at a Solution Lim t -> ∞ ∫ dx/xlnx from 1 to t u-substitution: u=lnx du=1/x dx Lim t -> ∞ ∫ 1/u du Lim t -> ∞ ln u Lim t -> ∞ ln(lnx) from 1 to t Lim t -> ∞...
  18. 9

    Convergent and Divergent Sequences

    Homework Statement Please look over my work and tell me if I did something wrong. Suppose Bn is a divergent sequence with the limit +∞, and c is a constant. Prove: lim cBn -> ∞ = +∞ for c > 0 Homework Equations N/A The Attempt at a Solution lim Bn -> ∞ = means that for some value K >...
  19. G

    Divergent limit + divergent limit = convergent limitIs it possible?

    Homework Statement As a part of Method of Frobenius, I am encountered with the following problems: Evaluate the following limits: Q1. \stackrel{limit}{_{x→0}}\frac{1-2x}{x} Q2. \stackrel{limit}{_{x→0}}\frac{x-1}{x} Q3. \stackrel{limit}{_{x→0}}\frac{1-2x}{x}+\frac{x-1}{x} In context of the...
  20. N

    Is this series convergent or divergent.

    Homework Statement Ʃ ne(-n2) Homework Equations The Attempt at a Solution I used the ratio test and wanted to know if the way I did it is correct or not |a(n+1) / a(n)| n+1 (e(-n2 -2n-1)) / n e(-n2) Now e-n^2 cancels and we get limn→∞ n+1/n * 1/(e2n)(e) After you take the limits you get...
  21. M

    Can a Divergent Free Vector Field be Expressed in a Certain Manner?

    hey pf! so if i have a vector field \vec{V} and i know \nabla \cdot \vec{V}=0 would i be able to express \vec{V} in the following manner: \vec{V}= \nabla \times \vec{f} for some \vec{f}since we know this automatically satisfies the divergent free requirement? if not, what must be...
  22. P

    Show that (-1)^n * (n/(n+1)) is divergent

    Homework Statement Using a proof by cases, show that (-1)^n * (n/(n+1)) is divergent Homework Equations A sequence a_n is said to be convergent if For every real number ε > 0, there exists a natural number N such that for all n > N, |a_n − L| < ε. The Attempt at a Solution Tried...
  23. Seydlitz

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  24. A

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  25. Fernando Revilla

    MHB Divergent sequence (Hanym's question at Yahoo Answers)

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  26. E

    Divergent Series: Finding the Largest Value of n

    Hi all, is there any way to find what the largest value of n is such that $$\sum_{k=1}^\infty\frac{1}{k^n}$$ is divergent? I don't need an answer, I need an approach to the problem.
  27. F

    Ratio test (convergent or divergent?)

    Homework Statement ∞ Ʃ n / 2^n n=1 Homework Equations ratio test lim |a(n+1) / a(n)| n->∞ The Attempt at a Solution I have the answer and the steps its just there's one part I am confused on, first I just apply n+1 to all my n terms, which gives me, ∞ Ʃ...
  28. D

    Convergent and divergent series

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  29. M

    Series Test for convergent and divergent

    Homework Statement Ʃ √n/(ln(n))^2 from n=2 to ∞ Homework Equations Series Test for convergent and divergent The Attempt at a Solution I tried doing ratio test and gotten [√(n+1)*(ln(n))^n] / [(ln(n+1))^(n+1) * √n] to find the limit, do...
  30. M

    Series Test for convergent and divergent

    Hello. I.m struggling to understand how to test for convergent and divergent. ∞ Ʃ (n/(n+1))^(n^2) n=1
  31. W

    Evaluate or show that is divergent

    Homework Statement evaluate or show that is divergent. Homework Equations \displaystyle\int_0^3 {\frac{1}{x-1}dx}The Attempt at a Solution \displaystyle\int_0^1 {\frac{1}{x-1}dx} +\displaystyle\int_1^3 {\frac{1}{x-1}dx}lim_{b->1^-} \displaystyle\int_0^b {\frac{1}{x-1}dx} + lim_{a->1^+}...
  32. Q

    A diff-invariant 1+1d QFT with divergent central charge?

    We know that a free scalar field on a diff-invariant 1+1 dimensional background (i.e. bosonic string theory on the worldsheet) contributes to the central charge of the Virasoro algebra with a constant term. Is there any examples of a 1+1d QFT that has instead a central charge contribution...
  33. M

    MHB Telling if a series is convergent or divergent?

    Just had a question from a coworker regarding how to tell if a series is convergent or divergent. Been a while since I've dealt with this so I thought I'd ask here. I *think* I remember that arithmatic series were convergent by nature, but a geometric series could be either convergent or...
  34. J

    Determine whether the integral is divergent. If convergent, evaluate.

    Homework Statement ∫ a= 2 b = ∞ (dv)/(v^2+7v-8) Homework Equations I have attempted the problem and am confused as to why the integral is not divergent. The Attempt at a Solution I integrated the function by using partial fractions and came up with a result of...
  35. A

    FLuid Flow through a Divergent Section

    Hi, Can Someone Elaborate the fluid(water) Characteristics Such as Velocity n pressure When it passes through a divergent Part. Actually The Fluid is pumped Out from A 0.5HP Centrifugal Pump and then made to pass through a Divergent Part.
  36. L

    Partition a divergent integral into finite values

    Hi there, I am reading an article, but I faced the following problem, and I am wondering if it is well known fact. If the integral of a function on some interval is infinity, can we partition this interval into countable disjoint (in their interiors) subintervals such that the integral...
  37. 0

    Proving the divergent integral of 1/f(x) as x-> infinity

    Homework Statement There exists a function f(x) such that the indefinite integral of 1/f(x) as x-> infinity diverges, and f(x) >= x for all values of x. Prove this function must be a linear polynomial. Homework Equations None that I know of.The Attempt at a Solution No idea where to start.
  38. J

    Proving That The Series is Convergent or Divergent

    Homework Statement Determine whether the following series converges or diverges: \sum_{}^{} ( \frac{1}{3} )^{ln(n)} Homework Equations N/A The Attempt at a Solution See attached document.. I had my Calc 2 final today, and this was our hard problem...but I don't know if my method is valid...
  39. J

    Example for divergent probability distribution ?

    Sometimes it is said that the probability distribution which does not add up to 1 still can be used to find relative probabilities. For example, consider probability distribution p_n = 1/n for all natural numbers. Does it make sense to say n = 1 is twice as probable as n=2, even if total...
  40. Z

    Can we simply truncate a Fourier series if it is divergent?

    can we simply truncate a Fourier series if it is divergent?? given a Fourier series of the form \sum_{n=0}^{\infty}\frac{cos(nx)}{\sqrt{n}} can i simply truncate this series up to some number finite N so i can get finite results ?? thanks.
  41. M

    Proving Whether an Alternating Series is Divergent or Convergent

    Homework Statement Determine an explicit function for this sequence and determine whether it is convergent. an={1, 0, -1, 0, 1, 0, -1, 0, 1, ...} The Attempt at a Solution I came up with this function: an = cos(nπ/2), and wrote that as sigma notation from n=0 to infinity. Is...
  42. S

    How to show sequnce is divergent (math. induction)

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  43. D

    MHB Show How to Prove Divergence of g'($\theta$)

    $$ g'(\theta) = 2\sum_{n = 1}^{\infty}(-1)^{n + 1}\cos n\theta. $$ How can I show that this series diverges for all values other than $\pm\frac{\pi}{2}$?
  44. M

    Explaining the Proof for Divergence of a Given Sequence

    Homework Statement Prove that the given sequence diverges to infinity. {an} = (-n^4+n^3+n)/(2n+7) Homework Equations Diverges definition The Attempt at a Solution So far I have: Let M>0 and let N= something. I'm having a hard time figuring out what N should equal for the...
  45. V

    Existence of divergent solutions to system of ODEs

    My question is in regards to systems of ordinary differential equations. One of my research topics right now involves working with some complicated coupled ODEs used to model ecological stuff. Without getting into the details, the model I am working on now has a bad tendency to diverge for...
  46. S

    Divergent Series - How to test it

    Homework Statement Ʃ (1+n+n2)/(√1+n2+n6)) n=1 to infinity Answer is divergentHomework Equations Comparison Test / P Series 0≤an≤bn The Attempt at a Solution Hello, I simplified the problem to Ʃ (1+n+n2)/(1+n2+n6)1/2 Is it incorrect of me to say immediately right here that because the power...
  47. K

    Series - convergent or divergent?

    Series -- convergent or divergent? 1. Determine whether the following series is convergent or divergent. When a series is convergent, find the sum. If it diverges, find if it is infinity, - inf, or DNE. Ʃ [(1/na) - 1/ (n+1)a] 2. we are finding if a >0 3. I know that it...
  48. B

    Gradient and Divergent Identities

    Homework Statement I need to show that ##\displaystyle\int_\Omega (\nabla G)w dxdy=-\int_\Omega (\nabla w) G dxdy+\int_\Gamma \hat{n} w G ds## given ##\displaystyle \int_\Omega \nabla F dxdy=\oint_\Gamma \hat{n} F ds## where ##\Omega## and ##\Gamma## are the domain and boundary respectively...
  49. K

    Determine Absolute Convergence, Conditionally Convergent, or Divergent

    Homework Statement ##\sum _{n=1}^{\infty }\dfrac {\left( -3\right) ^{n}} {n^{3}}## According to Wolfram Alpha the series diverges by the Limit Comparison Test, but I remember that the limit comparison only works with series greater than zero. How is this possible? Homework Equations...
  50. joe_cool2

    Is the series (n!)/(n^n) convergent or divergent?

    I am to find whether the sum of (n!)/(n^n) converges or diverges. I tried both the limit comparison test, and a regular comparison test. (These are the only types of tests I am allowed to use.) So I tried several approaches: Approach #1: (n!)/(n^n) > 1/(n^n) Normally we use a setup like...
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