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1 + 2 + 4 + 8 + ⋯

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In mathematics, is the infinite series whose terms are the successive powers of two. [1]

30 relations: Analytic continuation, Cesàro summation, Complex plane, Divergent series, Euler summation, Fixed point (mathematics), G. H. Hardy, Geometric series, Grandi's series, Infinity, Integer, Leonhard Euler, Mathematical proof, Mathematics, Möbius transformation, P-adic number, Power of two, Power series, Radius of convergence, Real number, Repeating decimal, Riemann sphere, Series (mathematics), Two's complement, 0.999..., 1 + 1 + 1 + 1 + ⋯, 1 + 2 + 3 + 4 + ⋯, 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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Cesàro summation

In mathematical analysis, Cesàro summation (also known as the Cesàro mean) assigns values to some infinite sums that are not convergent in the usual sense.

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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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Complex plane

In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the perpendicular imaginary axis.

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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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Euler summation

In the mathematics of convergent and divergent series, Euler summation is a summability method.

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Fixed point (mathematics)

In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is an element of the function's domain that is mapped to itself by the function.

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G. H. Hardy

Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis.

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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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Infinity

Infinity (symbol) is a concept describing something without any bound or larger than any natural number.

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Integer

An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

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Leonhard Euler

Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.

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Mathematical proof

In mathematics, a proof is an inferential argument for a mathematical statement.

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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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Möbius transformation

In geometry and complex analysis, a Möbius transformation of the complex plane is a rational function of the form of one complex variable z; here the coefficients a, b, c, d are complex numbers satisfying ad − bc ≠ 0.

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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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Power of two

In mathematics, a power of two is a number of the form where is an integer, i.e. the result of exponentiation with number two as the base and integer as the exponent.

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Power series

In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant.

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Radius of convergence

In mathematics, the radius of convergence of a power series is the radius of the largest disk in which the series converges.

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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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Repeating decimal

A repeating or recurring decimal is decimal representation of a number whose digits are periodic (repeating its values at regular intervals) and the infinitely-repeated portion is not zero.

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Riemann sphere

In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane, the complex plane plus a point at infinity.

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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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Two's complement

Two's complement is a mathematical operation on binary numbers, best known for its role in computing as a method of signed number representation.

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0.999...

In mathematics, 0.999... (also written 0., among other ways), denotes the repeating decimal consisting of infinitely many 9s after the decimal point (and one 0 before it).

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1 + 1 + 1 + 1 + ⋯

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.

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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 − 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 + 2 + 4 + 8, 1 + 2 + 4 + 8 +, 1 + 2 + 4 + 8 + ..., 1 + 2 + 4 + 8 + · · ·, 1 + 2 + 4 + 8 + …, 1+2+4+8, 1+2+4+8+, 1+2+4+8+..., 1+2+4+8+…, 1+2+4+8....

References

[1] https://en.wikipedia.org/wiki/1_%2B_2_%2B_4_%2B_8_%2B_⋯

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