Product
The product of the members of a finite arithmetic progression with an initial element a1, common differences d, and n elements in total is determined in a closed expression
where denotes the rising factorial and denotes the Gamma function. (Note however that the formula is not valid when is a negative integer or zero.)
This is a generalization from the fact that the product of the progression is given by the factorial and that the product
for positive integers and is given by
Taking the example from above, the product 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 product:
“Good is a product of the ethical and spiritual artistry of individuals; it cannot be mass-produced.”
—Aldous Huxley (1894–1963)
“Out of the thousand writers huffing and puffing through movieland there are scarcely fifty men and women of wit or talent. The rest of the fraternity is deadwood. Yet, in a curious way, there is not much difference between the product of a good writer and a bad one. They both have to toe the same mark.”
—Ben Hecht (1893–1964)
“Labor is work that leaves no trace behind it when it is finished, or if it does, as in the case of the tilled field, this product of human activity requires still more labor, incessant, tireless labor, to maintain its identity as a “work” of man.”
—Mary McCarthy (1912–1989)