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:
“In fast-moving, progress-conscious America, the consumer expects to be dizzied by progress. If he could completely understand advertising jargon he would be badly disappointed. The half-intelligibility which we expect, or even hope, to find in the latest product language personally reassures each of us that progress is being made: that the pace exceeds our ability to follow.”
—Daniel J. Boorstin (b. 1914)
“A gentleman opposed to their enfranchisement once said to me, “Women have never produced anything of any value to the world.” I told him the chief product of the women had been the men, and left it to him to decide whether the product was of any value.”
—Anna Howard Shaw (1847–1919)
“The seashore is a sort of neutral ground, a most advantageous point from which to contemplate this world. It is even a trivial place. The waves forever rolling to the land are too far-traveled and untamable to be familiar. Creeping along the endless beach amid the sun-squall and the foam, it occurs to us that we, too, are the product of sea-slime.”
—Henry David Thoreau (1817–1862)