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  2. 1 + 2 + 3 + 4 + ⋯ - ⋯ - Wikipedia

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

    where f (2k−1) is the (2k − 1)th derivative of f and B 2k is the (2k)th Bernoulli number: B 2 = ⁠ 1 / 6 ⁠, B 4 = ⁠− + 1 / 30 ⁠, and so on. Setting f ( x ) = x , the first derivative of f is 1, and every other term vanishes, so [ 15 ]

  3. International Mathematical Olympiad - Wikipedia

    en.wikipedia.org/wiki/International_Mathematical...

    The content ranges from extremely difficult algebra and pre-calculus problems to problems in branches of mathematics not conventionally covered in secondary or high school and often not at university level either, such as projective and complex geometry, functional equations, combinatorics, and well-grounded number theory, of which extensive knowledge of theorems is required.

  4. 1 − 2 + 3 − 4 + ⋯ - ⋯ - Wikipedia

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

    The first 15,000 partial sums of 0 + 12 + 3 − 4 + ... The graph is situated with positive integers to the right and negative integers to the left.

  5. Correlation - Wikipedia

    en.wikipedia.org/wiki/Correlation

    The correlation coefficient is +1 in the case of a perfect direct (increasing) linear relationship (correlation), −1 in the case of a perfect inverse (decreasing) linear relationship (anti-correlation), [5] and some value in the open interval (,) in all other cases, indicating the degree of linear dependence between the variables. As it ...

  6. World Series Formula V8 3.5 - Wikipedia

    en.wikipedia.org/wiki/World_Series_Formula_V8_3.5

    Formula Renault 3.5 Series at Donington Park in 2007.. The series came out of the Spanish Formula Renault Championship, which ran from 1991 to 1997.The World Series was founded as Open Fortuna by Nissan in 1998, and was mostly based in Spain, but visited other countries throughout its history, including France, Italy, Portugal and Brazil.

  7. Duolingo - Wikipedia

    en.wikipedia.org/wiki/Duolingo

    The Duolingo English Test (DET) is an online English proficiency test that measures proficiency in reading, writing, speaking, and listening in English. It is a computer-based test scored on a scale of 10–160, with scores above 120 considered English proficiency. The test's questions algorithmically adjust to the test-takers' ability level.

  8. Comparison of Portuguese and Spanish - Wikipedia

    en.wikipedia.org/wiki/Comparison_of_Portuguese...

    While the majority of lexical differences between Spanish and Portuguese come from the influence of the Arabic language on Spanish vocabulary, [1] [2] most of the similarities and cognate words in the two languages have their origin in Latin, [3] but several of these cognates differ, to a greater or lesser extent, in meaning.

  9. Islam - Wikipedia

    en.wikipedia.org/wiki/Islam

    Most estimates indicate China has approximately 20 to 30 million Muslims (1.5% to 2% of the population). [ 309 ] [ 310 ] Islam in Europe is the second-largest religion after Christianity in many countries, with growth rates due primarily to immigration and higher birth rates of Muslims in 2005, [ 311 ] accounting for 4.9% of all of Europe's ...