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:
“The history of literature—take the net result of Tiraboshi, Warton, or Schlegel,—is a sum of a very few ideas, and of very few original tales,—all the rest being variation of these.”
—Ralph Waldo Emerson (1803–1882)
“The ornament is a statuette, a black figure of a bird. I am prepared to pay on behalf of the figure’s rightful owner the sum of $5000 for its recovery. I am prepared to promise, to promise ... what is the phrase?—’No questions will be asked.’”
—John Huston (1906–1987)
“The sum and substance of female education in America, as in England, is training women to consider marriage as the sole object in life, and to pretend that they do not think so.”
—Harriet Martineau (1802–1876)