Definitions for absolute convergence
ab·so·lute con·ver·gence

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1. Absolute convergence

   In mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute values of the summands is finite. More precisely, a real or complex series ∑ n = 0 ∞ a n {\displaystyle \textstyle \sum _{n=0}^{\infty }a_{n}} is said to converge absolutely if ∑ n = 0 ∞ | a n | = L {\displaystyle \textstyle \sum _{n=0}^{\infty }\left|a_{n}\right|=L} for some real number L {\displaystyle \textstyle L} . Similarly, an improper integral of a function, ∫ 0 ∞ f ( x ) d x {\displaystyle \textstyle \int _{0}^{\infty }f(x)\,dx} , is said to converge absolutely if the integral of the absolute value of the integrand is finite—that is, if ∫ 0 ∞ | f ( x ) | d x = L . {\displaystyle \textstyle \int _{0}^{\infty }\left|f(x)\right|dx=L.} Absolute convergence is important for the study of infinite series because its definition is strong enough to have properties of finite sums that not all convergent series possess, yet is broad enough to occur commonly. (A convergent series that is not absolutely convergent is called conditionally convergent.) Absolutely convergent series behave "nicely". For instance, rearrangements do not change the value of the sum. This is not true for conditionally convergent series: The alternating harmonic series 1 − 1 2 + 1 3 − 1 4 + 1 5 − 1 6 + ⋯ {\textstyle 1-{\frac {1}{2}}+{\frac {1}{3}}-{\frac {1}{4}}+{\frac {1}{5}}-{\frac {1}{6}}+\cdots } converges to ln ⁡ 2 {\displaystyle \ln 2} , while its rearrangement 1 + 1 3 − 1 2 + 1 5 + 1 7 − 1 4 + ⋯ {\textstyle 1+{\frac {1}{3}}-{\frac {1}{2}}+{\frac {1}{5}}+{\frac {1}{7}}-{\frac {1}{4}}+\cdots } (in which the repeating pattern of signs is two positive terms followed by one negative term) converges to 3 2 ln ⁡ 2 {\textstyle {\frac {3}{2}}\ln 2} .

How to pronounce absolute convergence?

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Numerology

1. Chaldean Numerology

   The numerical value of absolute convergence in Chaldean Numerology is: 8

2. Pythagorean Numerology

   The numerical value of absolute convergence in Pythagorean Numerology is: 8

References

1. ^ Wikipedia
   https://en.wikipedia.org/wiki/Absolute_Convergence