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. D

    Divergent tree level Feynman diagrams?

    Hi everybody! I'm a new Physics Forums user and hope someone could help me out with my minor dilemma. I'm a PhD student in mathematical/theoretical physics and I' working on the Boltzmann equation in QFT. Up to now, there was no major emphasis on Feynamn diagrams - the approach was rather more...
  2. W

    (2) questions on convergent and divergent

    1. A year after the leak began the chemical had spread 1500 meters from its source. After two years, the chemical had spread 900 meters more, and by the end of the third year, it had reached an additional 540 meters. a. If this pattern continues, how far will the spill have...
  3. F

    Is this series convergent or divergent?

    convergent or divergent?? Homework Statement i took a calc 2 quiz today and had a question on one of the. it's too late to correct what i did, but it's never too late to learn it for the final haha here is the problem they want us to find the sum of the series (below) from 1 to...
  4. T

    Is the Series Convergent or Divergent?

    Homework Statement Determine whether the series converges or diverges. \sum 3+7n / 6n Attempt : Comparison test : 3+7n / 6n < 7n / 6n 3+7n / 6n < (6/7)n since (6/7)n is a geometric series and is convergent is 3+7n / 6n convergent as well?
  5. T

    Another convergent and divergent

    Homework Statement Determine whether the series is convergent or divergent. \sum n5 / (n6 + 1)
  6. T

    Determine whether the series is convergent or divergent

    Homework Statement Determine whether the series is convergent or divergent. 1 + 1/8 + 1/27 + 1/64 + 1/125 ... Homework Equations The Attempt at a Solution I know this is convergent but not sure how to prove this mathematically.
  7. T

    Limit of a convergent series and a divergent sequence

    Homework Statement Show that if: lim_{k\to\infty}b_k\to+\infty, \sum_{k=1}^\infty a_k converges and, \sum_{k=1}^\infty a_k b_k converges, then lim_{m\to\infty} b_m \sum_{k=m}^\infty a_k = 0 Homework Equations The Attempt at a Solution I only have an idea why this is true--\sum a_k...
  8. G

    Regularizing a divergent integral with a test function or convergence factor

    I'm trying to understand a paper in which the authors use a number of test functions (are they the same as convergence factors) to make integrate unintegrable functions. Now here is my ignorant question: why is this acceptable? The product of the original function and the test function or...
  9. K

    How to show this series is divergent?

    I got a series in the following form \sum_{k=0}^\infty\dfrac{k!}{c^{2(k-1)}} where c is arbritary complex constant, how can I show this series is divergent? Thanks
  10. M

    A proof based on divergent series

    if we can proof an statement but we make use of a divergent series or integral to proof it.. would it be considered valid ?? for example using the theory of distributions or divergent series you can always prove the Riemann Functional equation.
  11. I

    Proving the Convergence of (y_n) Given a Properly Divergent Sequence (x_n)

    Homework Statement Suppose that (x_n) is a properly divergent sequence, and suppose that (x_n) is unbounded above. Suppose that there exists a sequence (y_n) such that limit (x_n * y_n) exists. Prove that (y_n) ===> 0. Homework Equations (x_n) ===> 0 <====> (1/x_n) ===> 0...
  12. F

    Convergent or Divergent?

    If a power series, \sumc(subk)*x^{k} diverges at x=-2, then it diverges at x=-3. True or False? I said true, but was confused by my reasoning. Does anyone have any suggestions?
  13. A

    Is (n!/n^n)*exp^n a Convergent or Divergent Summation?

    1)summation for n=0 to infinity for (n!/n^n)*exp^n. Can anyone help to prove whether this is convergent or divergent?
  14. N

    Determine whether series is convergent or divergent

    Homework Statement Determine whether or not the series \sum^{\infty}_{n=1} \frac{1}{\sqrt{n+1}+\sqrt{n}} converges. The Attempt at a Solution Assuming this diverges, I rationalize it to get get \sum^{\infty}_{n=1} \sqrt{n+1} - \sqrt{n}. How would I proceed further? Is this even the...
  15. C

    How to prove Carrier's rule for divergent series?

    http://en.wikipedia.org/wiki/George_F._Carrier" :confused:
  16. gn0m0n

    Mathematica Divergent Integral and Mathematica

    Hi, I am trying to calculate a double integral, in Mathematica it could be denoted Integrate[(x*y)/(x*y-m2/s2),{x,0,1},{y,0,1-x}] That is, \int\int\frac{xy}{(xy-m^{2}/s^{2})}dydx with boundaries y=0,y=1-x and x=0,x=1. m and s are constants, of course. Now, I get some fairly...
  17. M

    Resummation of divergent integrals.

    if we can obtain resummation methods for divergent series such as 1-1+1-1+1-1+1-1+... or 1!-2!+3!-4!+.. my question is why is there no method to deal with divergent integrals like \int_{0}^{\infty} dx x^{s-1} or \int_{0}^{\infty} dx (x+1)^{-1} (x^{3}+x)
  18. C

    Vector calculus. Divergent vector field.

    I don't even know where to start this one. I can do all the other problems in the section, but this one makes no sense
  19. G

    Divergent series and the limit of the nth term as n approaches infinity

    I'm looking for help with my conceptual understanding of part of the following: 1) If a series is convergent it's nth term approaches 0 as n approaches infinity This makes perfect sense to me. 2) If the nth term of a series does not approach 0 as n approaches infinity, the series is...
  20. P

    Divergent Harmonic Series, Convergent P-Series (Cauchy sequences)

    Homework Statement (a) Show that \sum \frac 1n is not convergent by showing that the partial sums are not a Cauchy sequence (b) Show that \sum \frac 1{n^2} is convergent by showing that the partial sums form a Cauchy sequenceHomework Equations Given epsilon>0, a sequence is Cauchy if there...
  21. S

    Is My Thinking Wrong About Convergent or Divergent?

    For lim n->infinity n^-(1+1/n), the p series test shows that it converges since (1+1/n) will be greater than 1, while doing a limit comparison test with 1/n gives 1 showing that it diverges since 1/n diverges. For which one is my thinking wrong about?
  22. N

    Series- convergent or divergent?

    from n=1 to infinity does the series converge or diverge? n!/n^n its in the secition of the book with the comparison test and limit comparison test. if you compare it with 1/n^n (this is a geomoetric series) you get a= 1/n amd r= 1/n but in the thrm r = to some finite number...
  23. D

    Convergent and Divergent problem

    If I have (a_n + b_n)^n = c_n where a_n is convergent and b_n divergent. Is c_n then divergent? And what if a_n and b_n were divergent, would c_n be divergent also? but what if they were both convergent then surely c_n is convergent right? I can't see a rule or a theorem that tells me...
  24. R

    Convergent or divergent, p-series.

    Homework Statement Problem is to determine if this is convergent or divergent: n = 1 E infinity (27 + pi) / sqrt(n) Homework Equations p-series test? The Attempt at a Solution I was looking at this problem, It looks as if the p-series may apply, it is continuous, decreasing...
  25. K

    Renormalization and divergent integrals.

    If the problem of renormalization is that there are divergent integrals for x-->oo couldn't we make the change. \int_{0}^{\infty}dx f(x) \approx \sum_{n=0}^{\infty}f(nj) using rectangles with base 'j' small , and approximating the divergent integral by a divergent series and 'summing' by...
  26. K

    How Can Divergent Integrals Be Handled with Ramanujan Summation?

    Are there any method to deal with divergent integrals in the form \int_{0}^{\infty}dx \frac{x^{3}}{x+1} \int_{0}^{\infty}dx \frac{x}{(x+1)^{1/2}} ? in the same sense there are methods to give finite results to divergent series as 1+2+3+4+5+6+7+... or 1-4+9-16+25 or similar
  27. I

    Find Limit of Sequence: 6/7 or Divergent?

    Homework Statement Find the limit of sequence if it converges; otherwise indicate divergence. a_n=(5-9n+6n^4)/(7n^4+5n^3-3) answers a=6/7 b=-2 c=5/7 d=diverges Homework Equations none The Attempt at a Solution The limit of A_n is equal to 6/7 which is one of the...
  28. Gib Z

    Ramanujan Summation & Riemann Zeta Function: Negative Values

    I was wondering if anyone could tell me more about the Riemann Zeta function, esp at negative values. Especially when \sum_{n=1}^{\infty}n= \frac{-1}{12} R where R is the Ramanujan Summation Operator. Could anyone post a proof?
  29. S

    Is the series covergent or divergent?

    is the series covergent or divergent? I want to know that is the following series convergent or divergent?? \sum \frac{2}{\sqrt{n}+1} when i apply divergent test to it, it comes equal to 0 , it means that divergent test gets failed. then how to solve it? which test i should apply...
  30. A

    Convergence of Integral with Divergent Function at 0+

    I want to know if the integral \int_0^{\infty} dx/(4x^3 + x^(1/3)) is convergent or divergent?Thanks
  31. E

    Are S(N) and the integral of x^p both divergent in the same way?

    let be the divergent series: 1^p+2^p+3^p+.....+N^p=S(N) with p>0 my question is..how i would prove that this series S would diverge in the form: S(N)=N^{p+1}/p+1 N--->oo for the cases P=1,2,3,... i can use their exact sum to prove it but for the general case i can not find any...
  32. E

    How Can Renormalization Methods Remove Singularities in Divergent Series?

    let be the completely divergent series at \epsilon\rightarrow{0} in the form of: \sum_{n=0}^{\infty}\frac{a(n)g^{n}}{\epsilon^{n}} where g is the coupling constant of our theory..then let,s suppose this series is summable and that we can get the correct result S S=S(g,\epsilon) then...
  33. T

    Is sin convergent or divergent

    I just have a quick question, is cos and sin divergent or convergent? I keep getting mixed results from different sources. I know that both functions oscillate so on the interval [0, infinity) they both diverge. But for some of my homework problems relating to improper integrals, the book...
  34. happyg1

    Diverging Series: Proving Logarithmic Divergence with Real x

    Hello, I'm working on this problem: Prove that for any real x, the series SUM n=2 to infinity of 1/(log n)^x diverges. So far, I have applied the test that says that if SUM 2^n*a_2n converges then the series converges. I got: 1/log2*SUM 2^n/n^x I know that 1/n^x converges if x>1, but...
  35. E

    Divergent series in perturbation theory of quantum field theory

    if we know that the divergent series in perturbation theory of quantum field theory goes in the form: \sum_{n=0}^{\infty}a(n)g^{n}\epsilon^{-n} with \epsilon\rightarrow{0} then ..how would we apply the renormalization procedure to eliminate the divergences and obtain finite...
  36. S

    Evaluation of a divergent series?

    Hello, according to theory of alternating series, the series \sum_{n=0}^\infty (-1)^n is not convergent, correct?. Howcome maple estimates it as \sum_{n=0}^\infty (-1)^n = 0.5000000000. This seems strange to me.. Why this strange result?
  37. happyg1

    Proving Divergent Series: 1 + 1/3 + 1/5 + 1/7 +...

    Hi, I need to show that the infinite series 1+ 1/3 + 1/5 + 1/7 + 1/9 + ... diverges. Am I correct in saying that it is a subsequence of the divergent harmonic series, therefore diverges? Is there some other more elaborate (and correct) way of grouping the terms to show that they are greater...
  38. P

    What is the Correct Integral Value for Divergent or Convergent?

    \int_9^{inf} \frac{1}{x^{6/5}} first thing i did was found the integral of the function \frac{5}{x^{-1/5}} then plug in inf(i will name it b) and 9 \frac{5}{b^{-1/5}} - \frac{5}{9^{-1/5}} now i will find the lim -> inf well for \frac{5}{9^{-1/5}}, it's equal to 7.759 now for...
  39. C

    Integrating an Improper Divergent Integral & Ellipsoid Volume

    I need help with two questions. Find a divergent improper integral whose value is neither infinity nor -infinity. 2. Find the volume of an ellipsoid (a^2*x^2) + (b^2*8y^2) + (c^2*z^2) = a^2*b^2*c^2 using integration.
  40. S

    Convergent field, divergent potential?

    If you want to calculate the electric field at a distance r from a line of infinite length and uniform charge density you could one of three things: 1. Employ symmetry and Gauss' law. 2. Use superposition and integrate from minus to plus infinity along the rod. 3. Integrate to find the...
  41. E

    Divergent nozzle problem (find velocity)

    Determine change in velocity across ideal divergent nozzle with inlet enthalpy of 1,204 Btu/lbm and exit enthalpy of 1,203.91 Btu/lbm I know that delta v^2=(.09btu/lb)*(2)*(32.2lbm*ft/lbf sec^2)(778ftlbf/btu) so: deltav^2=4509.29ft^2/sec^2 taking the sqrt deltav=67.15ft/sec My...
  42. E

    Resumation of Divergent series

    How is this made?..in fact from having infinites you sum them and have a finite number...i do not know how you can do it..what techniques of maths are used.and if this would be valid for making any series convergent or have a finite number...i think you use divergent series math theories..could...
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