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:
“To die proudly when it is no longer possible to live proudly. Death freely chosen, death at the right time, brightly and cheerfully accomplished amid children and witnesses: then a real farewell is still possible, as the one who is taking leave is still there; also a real estimate of what one has wished, drawing the sum of one’s life—all in opposition to the wretched and revolting comedy that Christianity has made of the hour of death.”
—Friedrich Nietzsche (1844–1900)
“Without doubt God is the universal moving force, but each being is moved according to the nature that God has given it.... He directs angels, man, animals, brute matter, in sum all created things, but each according to its nature, and man having been created free, he is freely led. This rule is truly the eternal law and in it we must believe.”
—Joseph De Maistre (1753–1821)
“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)