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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 ...
The equals sign ( British English) or equal sign ( American English ), also known as the equality sign, is the mathematical symbol =, which is used to indicate equality in some well-defined sense. [ 1] In an equation, it is placed between two expressions that have the same value, or for which one studies the conditions under which they have the ...
Grandi's series. In mathematics, the infinite series 1 − 1 + 1 − 1 + ⋯, 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 ...
Raymond "Ray" William Johnson (born 1981 or 1982) [1] is an American internet celebrity best known for his eponymous YouTube channel and his web series on that channel, Equals Three. In 2013, the channel surpassed 10 million subscribers and had over 2 billion views, making it one of the most watched and subscribed to channels at the time.
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.
[1] [2] The three laws of motion were first stated by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), originally published in 1687. [3] Newton used them to investigate and explain the motion of many physical objects and systems.
Calculus. In mathematics, the harmonic series is the infinite series formed by summing all positive unit fractions : The first terms of the series sum to approximately , where is the natural logarithm and is the Euler–Mascheroni constant. Because the logarithm has arbitrarily large values, the harmonic series does not have a finite limit: it ...
One half is a rational number that lies midway between nil and unity (which are the elementary additive and multiplicative identities) as the quotient of the first two non-zero integers, . It has two different decimal representations in base ten, the familiar and the recurring , with a similar pair of expansions in any even base; while in odd ...