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  2. 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 with first term 1 4 and common ratio 1 4 ...

  3. 1/2 + 1/4 + 1/8 + 1/16 + ⋯ - Wikipedia

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

    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, this may be expressed as. The series is related to philosophical questions considered in antiquity, particularly ...

  4. List of commercial video games released as freeware - Wikipedia

    en.wikipedia.org/wiki/List_of_commercial_video...

    The Sims 2 (2004), a life simulation game by Maxis and Electronic Arts. It was released as freeware for a limited time on Origin on July 16, 2014, to celebrate the 10th anniversary of The Sims 2. It was removed from Origin on July 31, 2014. The Suffering (2004), a horror third/first person shooter developed by Surreal Software and published by ...

  5. List of Johnny Test episodes - Wikipedia

    en.wikipedia.org/wiki/List_of_Johnny_Test_episodes

    The following is a list of episodes for the animated television series Johnny Test . On June 11, 2013, Teletoon announced that the series had been renewed for a seventh season, to consist of 13 episodes and a three-part special. [1] However, in response to a tweet on June 25, 2015, regarding a seventh season, voice actor James Arnold Taylor ...

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  7. 1 − 2 + 4 − 8 + ⋯ - Wikipedia

    en.wikipedia.org/wiki/1_%E2%88%92_2_%2B_4_%E2%88...

    12 + 4 − 8 + ⋯. In mathematics, 12 + 4 − 8 + ⋯ is the infinite series whose terms are the successive powers of two with alternating signs. As a geometric series, it is characterized by its first term, 1, and its common ratio, −2. As a series of real numbers, it diverges. So in the usual sense it has no sum.

  8. 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 ...

  9. Grandi's series - Wikipedia

    en.wikipedia.org/wiki/Grandi's_series

    Grandi's series. In mathematics, the infinite series 11 + 11 + ⋯, also written. is sometimes called Grandi's series, after Italian mathematician, philosopher, and priest Guido Grandi, who gave a memorable treatment of the series in 1703. It is a divergent series, meaning that it does not have a sum. However, it can be manipulated to ...

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