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1 + 1 + 1 + 1 + ⋯

Index 1 + 1 + 1 + 1 + ⋯

In mathematics,, also written,, or simply, is a divergent series. [1]

Table of Contents

  1. 26 relations: Analytic continuation, Andrei Slavnov, Divergent series, Division by zero, 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 + ⋯.

  2. Arithmetic series
  3. Divergent series
  4. Geometric series
  5. Mathematical paradoxes

Analytic continuation

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

See 1 + 1 + 1 + 1 + ⋯ and Analytic continuation

Andrei Slavnov

Andrei Alekseevich Slavnov (Андрей Алексеевич Славнов; 22 December 1939 – 25 August 2022) was a Russian theoretical physicist, known for Slavnov–Taylor identities.

See 1 + 1 + 1 + 1 + ⋯ and Andrei Slavnov

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.

See 1 + 1 + 1 + 1 + ⋯ and Divergent series

Division by zero

In mathematics, division by zero, division where the divisor (denominator) is zero, is a unique and problematic special case.

See 1 + 1 + 1 + 1 + ⋯ and Division by zero

Emilio Elizalde

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

See 1 + 1 + 1 + 1 + ⋯ and Emilio Elizalde

Extended real number line

In mathematics, the extended real number system is obtained from the real number system \R by adding two infinity elements: +\infty and -\infty, where the infinities are treated as actual numbers.

See 1 + 1 + 1 + 1 + ⋯ and Extended real number line

Francisco José Ynduráin

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

See 1 + 1 + 1 + 1 + ⋯ and Francisco José Ynduráin

Geometric series

In mathematics, a geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms.

See 1 + 1 + 1 + 1 + ⋯ and Geometric series

Grandi's series

In mathematics, the infinite series, also written is sometimes called Grandi's series, after Italian mathematician, philosopher, and priest Guido Grandi, who gave a memorable treatment of the series in 1703. 1 + 1 + 1 + 1 + ⋯ and Grandi's series are 1 (number), divergent series, geometric series and mathematical paradoxes.

See 1 + 1 + 1 + 1 + ⋯ and Grandi's series

Harmonic series (mathematics)

In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions: \sum_^\infty\frac. 1 + 1 + 1 + 1 + ⋯ and harmonic series (mathematics) are divergent series.

See 1 + 1 + 1 + 1 + ⋯ and Harmonic series (mathematics)

Limit of a sequence

As the positive integer n becomes larger and larger, the value n\times \sin\left(\tfrac1\right) becomes arbitrarily close to 1.

See 1 + 1 + 1 + 1 + ⋯ and Limit of a sequence

Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

See 1 + 1 + 1 + 1 + ⋯ and Mathematics

Monotonic function

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

See 1 + 1 + 1 + 1 + ⋯ and Monotonic function

P-adic number

In number theory, given a prime number, the -adic numbers form an extension of the rational numbers which is distinct from the real numbers, though with some similar properties; -adic numbers can be written in a form similar to (possibly infinite) decimals, but with digits based on a prime number rather than ten, and extending to the left rather than to the right.

See 1 + 1 + 1 + 1 + ⋯ and P-adic number

Rational number

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

See 1 + 1 + 1 + 1 + ⋯ and Rational number

Real number

In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.

See 1 + 1 + 1 + 1 + ⋯ and Real number

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.

See 1 + 1 + 1 + 1 + ⋯ and Residue (complex analysis)

Riemann zeta function

The Riemann zeta function or Euler–Riemann zeta function, denoted by the Greek letter (zeta), is a mathematical function of a complex variable defined as \zeta(s).

See 1 + 1 + 1 + 1 + ⋯ and Riemann zeta function

Series (mathematics)

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

See 1 + 1 + 1 + 1 + ⋯ and Series (mathematics)

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.

See 1 + 1 + 1 + 1 + ⋯ and Theoretical physics

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.

See 1 + 1 + 1 + 1 + ⋯ and Zeta function regularization

1 + 2 + 3 + 4 + ⋯

The infinite series whose terms are the natural numbers is a divergent series. 1 + 1 + 1 + 1 + ⋯ and 1 + 2 + 3 + 4 + ⋯ are Arithmetic series and divergent series.

See 1 + 1 + 1 + 1 + ⋯ and 1 + 2 + 3 + 4 + ⋯

1 + 2 + 4 + 8 + ⋯

In mathematics, is the infinite series whose terms are the successive powers of two. 1 + 1 + 1 + 1 + ⋯ and 1 + 2 + 4 + 8 + ⋯ are divergent series and geometric series.

See 1 + 1 + 1 + 1 + ⋯ and 1 + 2 + 4 + 8 + ⋯

1 − 1 + 2 − 6 + 24 − 120 + ⋯

In mathematics, is a divergent series, first considered by Euler, that sums the factorials of the natural numbers with alternating signs. 1 + 1 + 1 + 1 + ⋯ and 1 − 1 + 2 − 6 + 24 − 120 + ⋯ are divergent series.

See 1 + 1 + 1 + 1 + ⋯ and 1 − 1 + 2 − 6 + 24 − 120 + ⋯

1 − 2 + 3 − 4 + ⋯

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

See 1 + 1 + 1 + 1 + ⋯ and 1 − 2 + 3 − 4 + ⋯

1 − 2 + 4 − 8 + ⋯

In mathematics, is the infinite series whose terms are the successive powers of two with alternating signs. 1 + 1 + 1 + 1 + ⋯ and 1 − 2 + 4 − 8 + ⋯ are divergent series and geometric series.

See 1 + 1 + 1 + 1 + ⋯ and 1 − 2 + 4 − 8 + ⋯

See also

Arithmetic series

Divergent series

Geometric series

Mathematical paradoxes

References

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

Also known as 1 + 1 + 1 + 1 + ..., 1 + 1 + 1 + 1 + 1 + · · ·, 1 + 1 + 1 + 1 + · · ·, 1+1+1+1+..., 1+1+1+···, Zeta(0).