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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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A £10 each-way single on a 10-1 selection in a horse race and paying 1 ⁄ 4 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)
For any integer n, n ≡ 1 (mod 2) if and only if 3n + 1 ≡ 4 (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 1–2–4 loop (the inverse of the 4–2–1 loop of the unaltered function f defined in the Statement of the problem section of ...
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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 ...
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.
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 ...