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

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

    1/4 + 1/16 + 1/64 + 1/256 + ⋯. Archimedes' figure with a = ⁠ 3 4 ⁠. In mathematics, the infinite series ⁠ 1 4 ⁠ + ⁠ 1 16 ⁠ + ⁠ 1 64 ⁠ + ⁠ 1 256 ⁠ + ⋯ is an example of one of the first infinite series to be summed in the history of mathematics; it was used by Archimedes circa 250–200 BC. [1] As it is a geometric series ...

  4. Four fours - Wikipedia

    en.wikipedia.org/wiki/Four_fours

    Four fours. Four fours is a mathematical puzzle, the goal of which is to find the simplest mathematical expression for every whole number from 0 to some maximum, using only common mathematical symbols and the digit four. No other digit is allowed. Most versions of the puzzle require that each expression have exactly four fours, but some ...

  5. 1 + 1 + 1 + 1 + ⋯ - Wikipedia

    en.wikipedia.org/wiki/1_%2B_1_%2B_1_%2B_1_%2B_%E...

    1 + 1 + 1 + 1 + ⋯ is a divergent series, meaning that its sequence of partial sums does not converge to a limit in the real numbers . The sequence 1 n can be thought of as a geometric series with the common ratio 1. For some other divergent geometric series, including Grandi's series with ratio −1, and the series 1 + 2 + 4 + 8 + ⋯ with ...

  6. 1,2,4-Triazole - Wikipedia

    en.wikipedia.org/wiki/1,2,4-Triazole

    1,2,4-Triazole is a planar molecule. The C-N and N-N distances fall into a narrow range 136 - 132 picometers, consistent with the aromaticity. [ 2 ] Although two tautomers can be envisioned, only one exists practically speaking. 1,2,4-Triazole is amphoteric, being susceptible to both N-protonation and deprotonation in aqueous solution.

  7. 1,2,3,4,6-Pentagalloyl glucose - Wikipedia

    en.wikipedia.org/wiki/1,2,3,4,6-Pentagalloyl_glucose

    1,2,3,4,6-Pentagalloylglucose is the penta gallic acid ester of glucose. It is a gallotannin and the precursor of ellagitannins. [1] Pentagalloyl glucose can precipitate proteins, [2] including human salivary α-amylase.

  8. 1,2,4-Trichlorobenzene - Wikipedia

    en.wikipedia.org/wiki/1,2,4-Trichlorobenzene

    The LD50 (oral, rats) is 756 mg/kg. Animal studies have shown that 1,2,4-trichlorobenzene affects the liver and kidney, and is possibly a teratogen. [4] There is no regulated occupational exposure limit for chemical exposure, but the National Institute for Occupational Safety and Health recommends no greater exposure than 5 ppm, over an 8-hour workday.

  9. Download, install, or uninstall AOL Desktop Gold - AOL Help

    help.aol.com/articles/aol-desktop-downloading...

    Download Desktop Gold. AOL Desktop Gold is included at no additional cost with your membership. 2. Under 'All Products' scroll to 'AOL Desktop Gold'. If you have an AOL Desktop Gold trial or subscription. Using the link in the Official AOL signup confirmation email you received. 1.