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  2. 1 + 2 + 3 + 4 + ⋯ - Wikipedia

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

    The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc.The nth partial sum is given by a simple formula: = = (+). This equation was known ...

  3. Formation (association football) - Wikipedia

    en.wikipedia.org/wiki/Formation_(association...

    The players of both teams are arranged in 235 formation. In association football, the formation of a team refers to the position players take in relation to each other on a pitch. As association football is a fluid and fast-moving game, a player's position (with the exception of the goalkeeper) in a formation does not define their role as ...

  4. Fibonacci sequence - Wikipedia

    en.wikipedia.org/wiki/Fibonacci_sequence

    Lucas numbers have L 1 = 1, L 2 = 3, and L n = L n−1 + L n−2. Primefree sequences use the Fibonacci recursion with other starting points to generate sequences in which all numbers are composite. Letting a number be a linear function (other than the sum) of the 2 preceding numbers. The Pell numbers have P n = 2P n−1 + P n−2.

  5. 1 − 2 + 3 − 4 + ⋯ - Wikipedia

    en.wikipedia.org/wiki/1_%E2%88%92_2_%2B_3_%E2%88...

    The idea becomes clearer by considering the general series 1 − 2x + 3x 24x 3 + 5x 4 − 6x 5 + &c. that arises while expanding the expression 1 ⁄ (1+x) 2, which this series is indeed equal to after we set x = 1.

  6. 1/2 + 1/4 + 1/8 + 1/16 + ⋯ - Wikipedia

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

    1/2 + 1/4 + 1/8 + 1/16 + ⋯. First six summands drawn as portions of a square. 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 ...

  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. 1, 2, 3, 4 (Plain White T's song) - Wikipedia

    en.wikipedia.org/wiki/1,_2,_3,_4_(Plain_White_T's...

    The music video for the song premiered on the MySpace main page January 16, 2009 [3] and was subsequently released on MTV, MTVU, VH1, Fuse, Music Choice and YouTube. [4] [5] [6] It found success on the weekly VH1 Top 20 Video Countdown, charting over five months straight between January and May, peaking at #5.

  9. List of prime numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_prime_numbers

    Some sequences have alternate names: 4n+1 are Pythagorean primes, 4n+3 are the integer Gaussian primes, and 6n+5 are the Eisenstein primes (with 2 omitted). The classes 10 n + d ( d = 1, 3, 7, 9) are primes ending in the decimal digit d .