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  2. 1 + 2 + 3 + 4 + ⋯ - Wikipedia

    en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E...

    The first four partial sums of the series 1 + 2 + 3 + 4 + ⋯.The parabola is their smoothed asymptote; its y-intercept is −1/12. [1]The infinite series whose terms ...

  3. Basel problem - Wikipedia

    en.wikipedia.org/wiki/Basel_problem

    The sum of the series is approximately equal to 1.644934. [3] The Basel problem asks for the exact sum of this series (in closed form ), as well as a proof that this sum is correct. Euler found the exact sum to be π 2 / 6 {\displaystyle \pi ^{2}/6} and announced this discovery in 1735.

  4. List of mathematical series - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_series

    2.4 Modified-factorial denominators. ... 7.2 Sum of reciprocal of factorials. 7.3 Trigonometry and ... 12 languages. العربية ...

  5. 1/2 + 1/4 + 1/8 + 1/16 + ⋯ - ⋯ - Wikipedia

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

    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

  6. Summation - Wikipedia

    en.wikipedia.org/wiki/Summation

    The summation of an explicit sequence is denoted as a succession of additions. For example, summation of [1, 2, 4, 2] is denoted 1 + 2 + 4 + 2, and results in 9, that is, 1 + 2 + 4 + 2 = 9. Because addition is associative and commutative, there is no need for parentheses, and the result is the same irrespective of the order of the summands ...

  7. Grandi's series - Wikipedia

    en.wikipedia.org/wiki/Grandi's_series

    (4) the result is ⁠ 1 / 2 ⁠ (3) the result is 1 (2) the result is infinite (30) no answer. The researcher, Giorgio Bagni, interviewed several of the students to determine their reasoning. Some 16 of them justified an answer of 0 using logic similar to that of Grandi and Riccati. Others justified ⁠ 1 / 2 ⁠ as being the average of 0 and 1 ...

  8. Aliquot sum - Wikipedia

    en.wikipedia.org/wiki/Aliquot_sum

    In number theory, the aliquot sum s(n) of a positive integer n is the sum of all proper divisors of n, that is, all divisors of n other than n itself. That is, = |,. It can be used to characterize the prime numbers, perfect numbers, sociable numbers, deficient numbers, abundant numbers, and untouchable numbers, and to define the aliquot sequence of a number.

  9. 1/4 + 1/16 + 1/64 + 1/256 + ⋯ - ⋯ - Wikipedia

    en.wikipedia.org/wiki/1/4_%2B_1/16_%2B_1/64_%2B...

    Today, a more standard phrasing of Archimedes' proposition is that the partial sums of the series 1 + ⁠ 1 / 4 ⁠ + ⁠ 1 / 16 ⁠ + ⋯ are: + + + + = +. This form can be proved by multiplying both sides by 1 − ⁠ 1 / 4 ⁠ and observing that all but the first and the last of the terms on the left-hand side of the equation cancel in pairs.