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:
“He was the product of an English public school and university. He was, moreover, a modern product of those seats of athletic exercise. He had little education and highly developed muscles—that is to say, he was no scholar, but essentially a gentleman.”
—H. Seton Merriman (1862–1903)
“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)
“Whenever a taboo is broken, something good happens, something vitalizing.... Taboos after all are only hangovers, the product of diseased minds, you might say, of fearsome people who hadn’t the courage to live and who under the guise of morality and religion have imposed these things upon us.”
—Henry Miller (1891–1980)