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  2. Geometric series - Wikipedia

    en.wikipedia.org/wiki/Geometric_series

    The geometric series is an infinite series derived from a special type of sequence called a geometric progression.This means that it is the sum of infinitely many terms of geometric progression: starting from the initial term , and the next one being the initial term multiplied by a constant number known as the common ratio .

  3. Geometric progression - Wikipedia

    en.wikipedia.org/wiki/Geometric_progression

    Examples of a geometric sequence are powers r k of a fixed non-zero number r, such as 2 k and 3 k. The general form of a geometric sequence is , , , , , … where r is the common ratio and a is the initial value. The sum of a geometric progression's terms is called a geometric series.

  4. List of sums of reciprocals - Wikipedia

    en.wikipedia.org/wiki/List_of_sums_of_reciprocals

    The sum of the reciprocals of the numbers in any sum-free sequence is less than 2.8570 . The sum of the reciprocals of the heptagonal numbers converges to a known value that is not only irrational but also transcendental, and for which there exists a complicated formula.

  5. Summation by parts - Wikipedia

    en.wikipedia.org/wiki/Summation_by_parts

    The formula for an integration by parts is () ′ = [() ()] ′ ().. Beside the boundary conditions, we notice that the first integral contains two multiplied functions, one which is integrated in the final integral (′ becomes ) and one which is differentiated (becomes ′).

  6. Arithmetico-geometric sequence - Wikipedia

    en.wikipedia.org/wiki/Arithmetico-geometric_sequence

    The nth element of an arithmetico-geometric sequence is the product of the nth element of an arithmetic sequence and the nth element of a geometric sequence. [1] An arithmetico-geometric series is a sum of terms that are the elements of an arithmetico-geometric sequence. Arithmetico-geometric sequences and series arise in various applications ...

  7. Ramanujan summation - Wikipedia

    en.wikipedia.org/wiki/Ramanujan_summation

    Ramanujan summation is a technique invented by the mathematician Srinivasa Ramanujan for assigning a value to divergent infinite series.Although the Ramanujan summation of a divergent series is not a sum in the traditional sense, it has properties that make it mathematically useful in the study of divergent infinite series, for which conventional summation is undefined.

  8. Today's Wordle Hint, Answer for #1244 on Thursday, November ...

    www.aol.com/todays-wordle-hint-answer-1244...

    If you’re stuck on today’s Wordle answer, we’re here to help—but beware of spoilers for Wordle 1244 ahead. Let's start with a few hints.

  9. 1/2 + 1/4 + 1/8 + 1/16 + ⋯ - ⋯ - Wikipedia

    en.wikipedia.org/wiki/1/2_%2B_1/4_%2B_1/8_%2B_1/...

    The geometric series on the real line. In mathematics, the infinite series ⁠ 1 / 2 ⁠ + ⁠ 1 / 4 ⁠ + ⁠ 1 / 8 ⁠ + ⁠ 1 / 16 ⁠ + ··· is an elementary example of a geometric series that converges absolutely. The sum of the series is 1. In summation notation, this may be expressed as

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