In mathematics, an infinite arithmetic series is an infinite series whose terms are in an arithmetic progression. Examples are 1 + 1 + 1 + 1 + · · · and 1 + 2 + 3 + 4 + · · ·. The general form for an infinite arithmetic series is
If a = b = 0, then the sum of the series is 0. If either a or b is nonzero, then the series diverges and has no sum in the usual sense.
Read more about Infinite Arithmetic Series: Zeta Regularization
Famous quotes containing the words infinite, arithmetic and/or series:
“Three elements go to make up an idea. The first is its intrinsic quality as a feeling. The second is the energy with which it affects other ideas, an energy which is infinite in the here-and-nowness of immediate sensation, finite and relative in the recency of the past. The third element is the tendency of an idea to bring along other ideas with it.”
—Charles Sanders Peirce (1839–1914)
“Your discovery of the contradiction caused me the greatest surprise and, I would almost say, consternation, since it has shaken the basis on which I intended to build my arithmetic.... It is all the more serious since, with the loss of my rule V, not only the foundations of my arithmetic, but also the sole possible foundations of arithmetic seem to vanish.”
—Gottlob Frege (1848–1925)
“Every man sees in his relatives, and especially in his cousins, a series of grotesque caricatures of himself.”
—H.L. (Henry Lewis)