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Divergent is a series of young adult science fiction adventure novels by American novelist Veronica Roth set in a post-apocalyptic dystopian Chicago. [1] The trilogy consists of Divergent (2011), Insurgent (2012), and Allegiant (2013).
More generally, if the series for f only converges for large x but can be analytically continued to all positive real x, then one can still define the sum of the divergent series by the limit above. A series of this type is known as a generalized Dirichlet series ; in applications to physics, this is known as the method of heat-kernel ...
is used for the series, and, if it is convergent, to its sum. This convention is similar to that which is used for addition: a + b denotes the operation of adding a and b as well as the result of this addition, which is called the sum of a and b. Any series that is not convergent is said to be divergent or to diverge.
After the final Divergent film’s 2016 debut, many of the franchise’s stars have gone on — or continued — to have very successful acting careers. Based on Veronica Roth’s book series of ...
Divergent is the debut novel of American novelist Veronica Roth, published by HarperCollins Children's Books in 2011. The first in the Divergent series, a trilogy of young adult dystopian novels (plus a book of short stories), [1] the novel is set in a post-apocalyptic Chicago, where society defines its citizens by their social and personality-related affiliation with one of five factions.
Roth wrote her first book, Divergent, while on winter break in her senior year at Northwestern University, and found an agent by the following March. [4] [9] [11] Her career took off rapidly with the novel's success; the publishing rights sold before she graduated from college in 2010 and the film rights sold mid-March 2011, before the novel was printed in April 2011.
A series is said to be convergent if the sequence consisting of its partial sums, (), is convergent; otherwise it is divergent. The sum of a convergent series is defined as the number s = lim n → ∞ s n {\textstyle s=\lim _{n\to \infty }s_{n}} .
This integral converges for all z ≥ 0, so the original divergent series is Borel summable for all such z. This function has an asymptotic expansion as z tends to 0 that is given by the original divergent series. This is a typical example of the fact that Borel summation will sometimes "correctly" sum divergent asymptotic expansions. Again, since