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. E

    Determine Convergent or Divergent

    an = [cos (3n) )] /n.cos(1/n) My solution is , I wrote an as liman→∞ [cos (3n) )] /[ cos(1/n) / (1/n) ) . We get liman→∞ cos(3n) / ( 1/0 ) . I think solution of this limit is zero but ı'm not sure cos(3n) .I think cos(3n) as a number and number/infinity is zero .As a result of...
  2. S

    Using comparison theorem to show if an integral is convergent or divergent

    Homework Statement use the comparison theorem to show that the integral of e^(-x^2) from 0 to infinity is convergent.Homework Equations None The Attempt at a Solution In class we have never dealt with using the comparison theorem with the exponential function so I was not sure what I function...
  3. chisigma

    MHB Prove Divergent Series of Positive Sequence | MathHelpForum.com

    From mathhelpforum.com... A constructive divergent series Let $\displaystyle \{x_{n}\}$ be a positive sequence satisfying $\lim_{\ n \rightarrow \infty} x_{n}= \infty$ Prove that the series $\displaystyle \sum_{n=1}^{\infty} (1-\frac{x_{n}}{x_{n+1}})$ is divergent. Till now no answers have...
  4. K

    Showing the sum of convergent and divergent sequence is divergent

    Homework Statement Show that the sum of a convrgent sequence and a divergent sequence must be a divergent sequence. What can you say about the sum of two divergent sequences? Homework Equations A theorem in the book states: Let {a_n} converge to a and {b_n} converge to b, then the...
  5. M

    Can the integral be made to converge by changing the variable?

    greetings . we have the integral : \lim_{T\to \infty }\int_{2-iT}^{2+iT}\frac{(s-1)^{n}}{s}ds which diverges for every value of n except n=0 if we perform the change of variables : s\rightarrow \frac{1}{s} then : \lim_{T\to \infty...
  6. B

    Prove a_n is divergent?

    Homework Statement Suppose that ∑a_n and ∑b_n are series with positive terms and ∑b_n is divergent. Prove that if: lim a_n/b_n = infinity n--->infinity then ∑a_n is also divergent.Homework Equations The Attempt at a Solution Well in attempting to write a viable solution, I have deducted...
  7. T

    Determine if integral is convergent or divergent?

    Homework Statement I attached the problem to this post. The Attempt at a Solution I was wondering if I could use the limit comparison test for this integral. My professor taught us this test that can be used for series but could it work for improper integrals as well? So what I would...
  8. H

    I just have a question about Uniqueness of Limits with divergent sequences.

    Homework Statement I'm supposed to answer true or false on whether or not the sequence ((-1)^n * n) tends toward both ±∞ Homework Equations Uniqueness of Limits The Attempt at a Solution I did prove it another way, but I would think that uniqueness of limits (as a definition...
  9. H

    Determine whether the series is convergent or divergent

    Homework Statement I have to find whether the following is Convergent or Divergent ∑ from n = 1 to infinity 2 / n(2n + 2)^(1/4) Actually it's the fourth root, this is just easier to write. Homework Equations According to the front of the sheet it's a quiz on P-Series and Integral Test I'm...
  10. T

    Divergent alternating series problem

    Homework Statement If Ʃa_n is divergent, the absolute value of Ʃa_n is divergent. True or false. This is the main question I am trying to answer. I should be able to answer this problem on my own, but i ran into a problem that confused me. What I Did So I decided to start this...
  11. C

    Can a Convergent Series Prove the Divergence of Another Series?

    Homework Statement Suppose that ∑_(n=1)^∞▒a_n where a_n≠0 is known to be a convergent series. Prove that ∑_(n=1)^∞▒1/a_n is a divergent series. Homework Equations The Attempt at a Solution if ∑_(n=1)^∞▒a_n is convergent then lim n→∞ a_n = 0. thus for some N a_n>1 and a_n...
  12. W

    Is this series convergent or divergent

    Homework Statement Me and my friend are debating on wether the follow seris is convergent or divergent. The seris is the sum of (-1)^n-1 * ln(n)/n. Homework Equations p test and comparision tests. And alternating series test The Attempt at a Solution My approach to this problem...
  13. R

    Convergence and Divergence of the Sequence nsin(npi)

    I need to find out if this function is convergent or divergent when finding the limit to infiniti. nsin(npi) How do I solve this? Do I use the squeeze theorem or lhospital rule?
  14. H

    Proof on Sequences: Sum of a convergent and divergent diverges

    Homework Statement Prove if sequence a_{n} converges and sequence b_{n} diverges, then the sequence a_{n}+b_{n} also diverges. Homework Equations The Attempt at a Solution My professor recommended a proof by contradiction. That is, suppose a_{n}+b_{n} does converge. Then, for...
  15. L

    To show that an integral is divergent

    Hi all I am looking for a simple way to show that the mean of the Cauchy distribution us undefined. This is because this integral diverges: \underset{-\infty}{\overset{\infty}{\int}}\frac{x}{x^{2}+a^{2}}dx Now, I know one proof which replaces the limits of integration with -x1 and x2. After...
  16. M

    Convergin and divergent lens, rare situations

    what happen if converging rays are made to pass to a convex lens? what happen if divergent rays are made to pass to a concave lens?
  17. B

    Divergent Series question

    (1) Using the Archimedean definition of divergence, prove that if \sum_{i=1}^{\infty }x_{i} diverges to infinity, then so does either \sum_{i=1}^{\infty }x_{2i} or \sum_{i=1}^{\infty }x_{2i+1}. (2) Show an example where \sum_{i=1}^{\infty }x_{i} diverges to infinity but \sum_{i=1}^{\infty...
  18. D

    A_n := n^(1/n) - 1 yields a divergent series

    Homework Statement I know that if a_n := n^{1/n} - 1, then \Sigma a_n is divergent. I know this (by the integral test) because the integral of 2^{1/n} - 1 from 1 to infinity is infinite. However, I want to avoid using non-elementary functions (here, the exponential integral) in my proof that...
  19. S

    Prove series is divergent (sqrt(n+1) - sqrt(n))/sqrt(n)

    Homework Statement Prove that \sum\limits_{n = 0}^\infty {\frac{{\left( { \sqrt{n+1} \right) - \sqrt{n} }}{{\left( {\sqrt{n}} \right)!}}} is divergent Homework Equations The Attempt at a Solution This is an intro to analysis course. We haven't gone over the integral test which would be...
  20. S

    How to show that this is divergent?

    Homework Statement Basically i have got the infinite sum of (n+2)1/2-n1/2 and i think it is divergent ( I hope) but i have no idea how to show it, the ratio test is not helpful and i cannot find anything to compare it with. Thanks in advance.
  21. T

    Convergent and Divergent Series

    Homework Statement For what integer k, k > 1, will both sigma n=1 to infinity ((-1)^(kn))/n and sigma n=1 to infinity (k/4)^n converge? A) 6 B) 5 C)4 D)3 E)2 Homework Equations The Attempt at a Solution I tried to use the ratio test and after some simplifying I got (-1)^k (n/n+1)...
  22. P

    How to determine if the series is convergent or divergent.

    Homework Statement Determine if the series is convergent or divergent. \sum x^2e^{-x^2} Homework Equations The Attempt at a Solution x^2e^{-x^2}=\frac{x^2}{e^{x^2}} \lim_{x\to\infty } \frac{(x+1)^2}{e^{(x+1)^2}}\frac{e^{x^2}}{x^2} and since (x+1)^2=x^2+2n+1 and...
  23. G

    Air flow in Convergent divergent nozzle

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  24. H

    Are These Infinite Series Convergent or Divergent?

    Homework Statement I have been straining to find convergence or divergence of a few infinite series. I have tried everything I can think of; ratio test, root test, trying to find a good series for comparison, etc. Here are the formulas for the terms: #1 1 ------------- (ln(n))^ln(n)...
  25. Z

    Zeta regularization of divergent integrals

    From the model used in the zeta regularization procedure to give a meaning to divergent series in the form 1+2+3+4+... , we propose a similar method to give a finite meaning to divergent integrals in the form \int_{0}^{\infty}dx x^{m} for positive 'm' in terms of the negative values of the...
  26. N

    Solving Divergent Integral: -infinity Correct?

    Homework Statement I had to solve the integral...After all my work i got -infinity 3 integral sign 1/ [(t-3)^4/3] 1 Homework Equations The Attempt at a Solution -infinity...is this correct? and would this be divergent?
  27. S

    Determine whether the series is convergent or divergent.

    Hello, I have to determine whether the series converges or diverges. It is \Sigma (-1)^n * cos(Pi/n) where n=1 and goes to infinity. First I took the absolute value of the function and got the limit from n to infinity of cos(pi/n) and as a result I got 1 because cos(0)=1. However my...
  28. C

    Series - Convergent or Divergent?

    Is the series convergent or divergent? n=1 summation and it goes to infinity n!/2n!+1 [Infinite series] Homework Equations None. The Attempt at a Solution I have no idea.
  29. J

    Explain why ∑(1+n)/(1+2n) is divergent

    Homework Statement As the title says. Homework Equations mentioned in solution The Attempt at a Solution Let Sn = {(1+1)/(1+2) , (1+2)/(1+4), (1+3)/(1+6), ...}. If ∑(1+n)/(1+2n) is convergent, then lim n-->∞ Sn = 0; to put it another way, there exists an N so that whenever n ≤...
  30. Z

    Regularization of a divergent integral in several variables

    i've got the following problem let be the integral \int_{R^{3}} dxdydz \frac{R(x,y,z)}{Q(x,y,z)} here R(x,y,z) and Q(x,y,z) are Polynomials on several variable. Let us suppose this integral is divergent, in order to regularize it i have thought about substracting several terms so...
  31. A

    Showing a sequence is divergent

    A sequence \{x_n\} in a metric space (X,d) converges iff (\exists x\in X)(\forall \epsilon > 0)(\exists N \in \mathbb N)(\forall n > N)(d(x_n,x) < \epsilon). Am I correct when I assert that the negation of this is: A sequence \{x_n\} does not converge in (X,d) iff (\forall x\in X)(\exists...
  32. F

    Is the Weibull Distribution Effective for β < 1 Despite Divergence at t=0?

    When the weibull shape parameter beta is <1, the pdf is divergent at t=0 due to negative exponent of beta -1. With such a divergent distribution is it meaningful to use Weibull for beta <1?
  33. Z

    Why are no DIVERGENT quantities (infinities) in String Theory ?

    Why are no DIVERGENT quantities (infinities) in String Theory ?? why String theory is FREE of infinities ?? ... why there are no divergent integrals in string theory whereas in normal Quantum Field theory there are infinities ??
  34. M

    Prove that the harmonic series is divergent

    Homework Statement Prove that the \sum1/n is divergent. Does anyone know a simple proof for this. I understand that it does not converge intuitively but I'm not sure how to prove it in symbols. Thank you for your help. M Homework Equations The Attempt at a Solution
  35. Z

    Use comparison theorem to show if integral is convergent or divergent

    Homework Statement int (e^-x)/(x)dx from 0 to infinity Determine if integral is convergent or divergent2. The attempt at a solution I assume because the bottom limit is 0 and there is an x in the bottom of the integral that this is going to be divergent but I still have to use the...
  36. C

    Two divergent series whose minimum converges?

    I am struggling to find two divergent series, \Sigmaan and \Sigmabn, such that the series of minimum terms, \Sigmamin{an,bn}, actually converges. A further stipulation is that both an and bn must be positive, decreasing sequences. (Otherwise the problem is trivial, as one could simply...
  37. N

    [QFT] Divergent Green's function?

    Homework Statement I am being asked to consider a Dirac spinor with two complex components and the following Lagrangian: L = L_{Dirac}-\stackrel{g}{4}{(\psi\bar{\psi})^{2}} I am asked to derive the Feynman rules for this theory which I can do using the standard methods. However, I am...
  38. L

    Convergent or Divergent Integral: Comparison Theorem

    Homework Statement Determine if the following is improper and convergent, improper and divergent, or proper \int \frac{dx}{\sqrt[3]{x^2 - 7}} from 8 to infinityThe Attempt at a Solution Since I don't know how to integrate...
  39. M

    Divergent partial wave amplitudes

    I want to calculate the partial wave amplitudes for various processes but get divergent results in certain cases which I assume is related to the propagator going on shell - the forward scattering amplitude is infinite. I guess I have to introduce some sort of cut but don't know how to do this...
  40. A

    Convergent and Divergent Integrals

    I had a question regarding convergent and divergent integrals. I want to know the "exact" definition of an improper integral that converges. Wikipedia states that For a while, I took that as a valid answer and claimed that any integral that has a finite answer must be convergent. However, I...
  41. R

    Determine whethere the following series is convergent or divergent

    Homework Statement Determine whether the following series is convergent or divergent: \frac{1}{2^2}+\frac{2^2}{3^3}+\frac{3^3}{4^4}+... I rewrite it as: \sum_{n=1}^{\infty} \frac{n^n}{(n+1)^{n+1}} Homework Equations The Attempt at a Solution I stopped. I can not do anything.
  42. L

    Is a series is convergent or divergent

    Homework Statement Determine the convergence or divergence of the series. If the series is convergent, find its sum. Justify each answer. (n=1, to infinity) \sum(7/9 + n^5) Help please? I missed a lot of school recently from being sick and need help with this!
  43. T

    Sum of convergent and divergent series

    Homework Statement Prove that if $\displaystyle\sum_{n=1}^\infty a_n$ converges and $\displaystyle\sum_{n=1}^\infty b_n$ diverges, then $\displaystyle\sum_{n=1}^\infty (a_n+b_n)$ diverges. Homework Equations I know that the limit of {a_n} = 0 because it is convergent, but I can't say...
  44. P

    Problem with divergent integral

    I'm confused with the following integral. Let a > 1. \int_{a}^{\infty} \left( \dfrac{1}{t} - \dfrac{1}{t-1} \right) ~ dt = \left[ \log \left| \dfrac{t}{t-1} \right| \right]_{a}^{\infty} = - \log \left| \dfrac{a}{a-1} \right| This should be the correct result. But I could also...
  45. T

    Proof: c * divergent sequence diverges

    Homework Statement Suppose that {a_n} is a divergent sequence of real numbers and c \in R, c <> 0. Prove that {c*a_n} diverges. Homework Equations The Attempt at a Solution I have attempted to solve the problem as a proof by contradiction, but am afraid I am leaving something out...
  46. Z

    Cauchy trick for divergent integrals.

    is this trick valid at least in the 'regularization' sense ?? for example \int_{-\infty}^{\infty} \frac{dx}{x^{2}-a^{2}} then we replace thi integral above by \int_{-\infty}^{\infty} \frac{dx}{x^{2}+ie-a^{2}} for 'e' tending to 0 using Cauchy residue theorem i get...
  47. Q

    Can the first few terms of a convergent infinite series diverge?

    I can't remember much from my intro. analysis class anymore. If you have an infinite series that ultimately converges, can the first few terms diverge (i.e., can they move away from the convergence point)? And if so, how many of these terms can do so? I'm trying to understand how to "get...
  48. S

    Is the series of c(1/2k) divergent?

    Homework Statement Show \sum_{k=1}^{\infty} c\k^(1\div2k, c is an element of [tex]\Re, c > 0, is divergent. Homework Equations 1/n is divergentThe Attempt at a Solution Finding a similar series and doing comparison test, is it right?
  49. I

    1-2+3-4 divergent series confusion

    How did Euler came up with a solution of 1/4 for the series 1-2+3-4... There is a wikipedia page explaining it, http://en.wikipedia.org/wiki/1_%E2%88%92_2_%2B_3_%E2%88%92_4_%2B_%C2%B7_%C2%B7_%C2%B7 but I'm not quite following the manipulation of the numbers. How is a 1 pulled out and...
  50. J

    Divergent Series: Rearranging for Convergence?

    Is it possible to re-arrange the terms of a divergent series such that the re-arranged series converges?
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