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1 + 1 + 1 + 1 + ⋯

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In mathematics,, also written \sum_^ n^0, \sum_^ 1^n, or simply \sum_^ 1, is a divergent series, meaning that its sequence of partial sums does not converge to a limit in the real numbers. [1]

25 relations: Analytic continuation, Andrei Slavnov, Divergent series, Emilio Elizalde, Extended real number line, Francisco José Ynduráin, Geometric series, Grandi's series, Harmonic series (mathematics), Limit of a sequence, Mathematics, Monotonic function, P-adic number, Rational number, Real number, Residue (complex analysis), Riemann zeta function, Series (mathematics), Theoretical physics, Zeta function regularization, 1 + 2 + 3 + 4 + ⋯, 1 + 2 + 4 + 8 + ⋯, 1 − 1 + 2 − 6 + 24 − 120 + ..., 1 − 2 + 3 − 4 + ⋯, 1 − 2 + 4 − 8 + ⋯.

Analytic continuation

In complex analysis, a branch of mathematics, analytic continuation is a technique to extend the domain of a given analytic function.

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Andrei Slavnov

Andrei Alekseevich Slavnov (Андрей Алексеевич Славнов, born 22 December 1939, Moscow) is a Russian theoretical physicist, known for Slavnov-Taylor identities.

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Christmas

Christmas is an annual festival commemorating the birth of Jesus Christ,Martindale, Cyril Charles.

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Christmas and holiday season

The Christmas season, also called the festive season, or the holiday season (mainly in the U.S. and Canada; often simply called the holidays),, is an annually recurring period recognized in many Western and Western-influenced countries that is generally considered to run from late November to early January.

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Christmas Eve

Christmas Eve is the evening or entire day before Christmas Day, the festival commemorating the birth of Jesus.

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Christmas traditions

Christmas traditions vary from country to country.

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Divergent series

In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit.

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Emilio Elizalde

Emilio Elizalde (born March 8, 1950) is a Spanish physicist working in the fields of gravitational physics and general relativity.

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Extended real number line

In mathematics, the affinely extended real number system is obtained from the real number system by adding two elements: and (read as positive infinity and negative infinity respectively).

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Francisco José Ynduráin

Francisco José Ynduráin Muñoz (23 December 1940 – 6 June 2008) was a Spanish theoretical physicist.

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Geometric series

In mathematics, a geometric series is a series with a constant ratio between successive terms.

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Grandi's series

In mathematics, the infinite series 1 - 1 + 1 - 1 + \dotsb, also written \sum_^ (-1)^n is sometimes called Grandi's series, after Italian mathematician, philosopher, and priest Guido Grandi, who gave a memorable treatment of the series in 1703.

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Harmonic series (mathematics)

In mathematics, the harmonic series is the divergent infinite series: Its name derives from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string are,,, etc., of the string's fundamental wavelength.

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Limit of a sequence

As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Monotonic function

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order.

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New Year

New Year is the time or day at which a new calendar year begins and the calendar's year count increments by one.

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New Year's Day

New Year's Day, also called simply New Year's or New Year, is observed on January 1, the first day of the year on the modern Gregorian calendar as well as the Julian calendar.

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New Year's Eve

In the Gregorian calendar, New Year's Eve (also known as Old Year's Day or Saint Sylvester's Day in many countries), the last day of the year, is on 31 December which is the seventh day of Christmastide.

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P-adic number

In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems.

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Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Residue (complex analysis)

In mathematics, more specifically complex analysis, the residue is a complex number proportional to the contour integral of a meromorphic function along a path enclosing one of its singularities.

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Riemann zeta function

The Riemann zeta function or Euler–Riemann zeta function,, is a function of a complex variable s that analytically continues the sum of the Dirichlet series which converges when the real part of is greater than 1.

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Series (mathematics)

In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity.

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Theoretical physics

Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena.

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Zeta function regularization

In mathematics and theoretical physics, zeta function regularization is a type of regularization or summability method that assigns finite values to divergent sums or products, and in particular can be used to define determinants and traces of some self-adjoint operators.

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1 + 2 + 3 + 4 + ⋯

The infinite series whose terms are the natural numbers is a divergent series.

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1 + 2 + 4 + 8 + ⋯

In mathematics, is the infinite series whose terms are the successive powers of two.

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1 − 1 + 2 − 6 + 24 − 120 + ...

In mathematics, the divergent series was first considered by Euler, who applied summability methods to assign a finite value to the series.

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1 − 2 + 3 − 4 + ⋯

In mathematics, 1 − 2 + 3 − 4 + ··· is the infinite series whose terms are the successive positive integers, given alternating signs.

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1 − 2 + 4 − 8 + ⋯

In mathematics, is the infinite series whose terms are the successive powers of two with alternating signs.

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2018

2018 has been designated as the third International Year of the Reef by the International Coral Reef Initiative.

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2019

2019 (MMXIX) will be a common year starting on Tuesday of the Gregorian calendar, the 2019th year of the Common Era (CE) and Anno Domini (AD) designations, the 19th year of the 3rd millennium, the 19th year of the 21st century, and the 10th and last year of the 2010s decade.

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1 + 1 + 1 + 1 + ..., 1 + 1 + 1 + 1 + 1 + · · ·, 1 + 1 + 1 + 1 + · · ·, 1 + 1 + 1 + 1 + …, 1+1+1+···.

References

[1] https://en.wikipedia.org/wiki/1_%2B_1_%2B_1_%2B_1_%2B_⋯

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