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:
“I was brought up to believe that the only thing worth doing was to add to the sum of accurate information in the world.”
—Margaret Mead (1901–1978)
“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)
“[M]y conception of liberty does not permit an individual citizen or a group of citizens to commit acts of depredation against nature in such a way as to harm their neighbors and especially to harm the future generations of Americans. If many years ago we had had the necessary knowledge, and especially the necessary willingness on the part of the Federal Government, we would have saved a sum, a sum of money which has cost the taxpayers of America two billion dollars.”
—Franklin D. Roosevelt (1882–1945)