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:
“[As teenager], the trauma of near-misses and almost- consequences usually brings us to our senses. We finally come down someplace between our parents’ safety advice, which underestimates our ability, and our own unreasonable disregard for safety, which is our childlike wish for invulnerability. Our definition of acceptable risk becomes a product of our own experience.”
—Roger Gould (20th century)
“Cultural expectations shade and color the images that parents- to-be form. The baby product ads, showing a woman serenely holding her child, looking blissfully and mysteriously contented, or the television parents, wisely and humorously solving problems, influence parents-to-be.”
—Ellen Galinsky (20th century)
“Junk is the ideal product ... the ultimate merchandise. No sales talk necessary. The client will crawl through a sewer and beg to buy.”
—William Burroughs (b. 1914)