Arithmetic Progression - Product

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)

    Poetry, whose material is language, is perhaps the most human and least worldly of the arts, the one in which the end product remains closest to the thought that inspired it.... Of all things of thought, poetry is the closest to thought, and a poem is less a thing than any other work of art ...
    Hannah Arendt (1906–1975)

    Man’s main task in life is to give birth to himself, to become what he potentially is. The most important product of his effort is his own personality.
    Erich Fromm (1900–1980)