Sum
This section is about Finite arithmetic series. For Infinite arithmetic series, see Infinite arithmetic series.The sum of the members of a finite arithmetic progression is called an arithmetic series.
Expressing the arithmetic series in two different ways:
Adding both sides of the two equations, all terms involving d cancel:
Dividing both sides by 2 produces a common form of the equation:
An alternate form results from re-inserting the substitution: :
In 499 AD Aryabhata, a prominent mathematician-astronomer from the classical age of Indian mathematics and Indian astronomy, gave this method in the Aryabhatiya (section 2.18).
So, for example, the sum of the terms of the arithmetic progression given by an = 3 + (n-1)(5) up to the 50th term is
Read more about this topic: Arithmetic Progression
Famous quotes containing the word sum:
“If the twentieth century is to be better than the nineteenth, it will be because there are among us men who walk in Priestley’s footsteps....To all eternity, the sum of truth and right will have been increased by their means; to all eternity, falsehoods and injustice will be the weaker because they have lived.”
—Thomas Henry Huxley (1825–95)
“the possibility of rule as the sum of rulelessness:”
—Archie Randolph Ammons (b. 1926)
“The more elevated a culture, the richer its language. The number of words and their combinations depends directly on a sum of conceptions and ideas; without the latter there can be no understandings, no definitions, and, as a result, no reason to enrich a language.”
—Anton Pavlovich Chekhov (1860–1904)