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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. [1]

## Émile Borel

Félix Édouard Justin Émile Borel (7 January 1871 – 3 February 1956) was a French mathematician and politician.

## Binomial transform

In combinatorics, the binomial transform is a sequence transformation (i.e., a transform of a sequence) that computes its forward differences.

## Borel summation

In mathematics, Borel summation is a summation method for divergent series, introduced by.

## Christian Wolff (philosopher)

Christian Wolff (less correctly Wolf,; also known as Wolfius; ennobled as Christian Freiherr von Wolff; 24 January 1679 – 9 April 1754) was a German philosopher.

## 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.

## Euler summation

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

## Finite difference

A finite difference is a mathematical expression of the form.

## Geometric series

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

## Gottfried Wilhelm Leibniz

Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.

## 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.

## Halle (Saale)

Halle (Saale) is a city in the southern part of the German state Saxony-Anhalt.

## Hanover

Hanover or Hannover (Hannover), on the River Leine, is the capital and largest city of the German state of Lower Saxony (Niedersachsen), and was once by personal union the family seat of the Hanoverian Kings of the United Kingdom of Great Britain and Ireland, under their title as the dukes of Brunswick-Lüneburg (later described as the Elector of Hanover).

## 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.

## Mathematics

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

## 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.

## Real number

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

## 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.

## 1

1 (one, also called unit, unity, and (multiplicative) identity) is a number, numeral, and glyph.

## 1/2 − 1/4 + 1/8 − 1/16 + ⋯

In mathematics, the infinite series is a simple example of an alternating series that converges absolutely.

## References

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