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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 ...

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  4. Each-way - Wikipedia

    en.wikipedia.org/wiki/Each-way

    A £10 each-way single on a 10-1 selection in a horse race and paying 14 the odds a place 1, 2, or 3 would cost £20. Returns on the win part of the bet would be £10 × (10/1 × 1) + stake = £110 (£100 winnings + £10 stake) Returns on the place part of the bet would be £10 × (10/4 × 1) + stake = £35 (£25 winnings + £10 stake)

  5. Collatz conjecture - Wikipedia

    en.wikipedia.org/wiki/Collatz_conjecture

    For any integer n, n ≡ 1 (mod 2) if and only if 3n + 14 (mod 6). Equivalently, ⁠ n − 1 / 3 ⁠ ≡ 1 (mod 2) if and only if n ≡ 4 (mod 6). Conjecturally, this inverse relation forms a tree except for the 124 loop (the inverse of the 421 loop of the unaltered function f defined in the Statement of the problem section of ...

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  7. College football conference tiebreakers will decide races ...

    www.aol.com/college-football-conference...

    Power Four conference races have three weeks left and many permutations that can take place along the way. A break down all the tiebreaker situations. ... (5-1), No. 25 Iowa State (4-2), No. 19 ...

  8. 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 2 − 4x 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.

  9. Why SMU edged out Alabama for final spot in College Football ...

    www.aol.com/why-smu-edged-alabama-final...

    The Crimson Tide were ranked at No. 4 compared to the Mustangs being at No. 13. Here's what CFP selection committee chair Warde Manuel said on Sunday on why the Mustangs won out the final seeding ...