Can Arithmetic Series Be Infinite?

The behavior of the arithmetic sequence depends on the common difference d . Arithmetic sequences can be finite or infinite.

Can you have an infinite arithmetic series?

An arithmetic sequence is a sequence in which the difference between each consecutive term is constant. The sum of an infinite arithmetic sequence is either ∞, if d > 0, or - ∞, if d < 0. ... There are two ways to find the sum of a finite arithmetic sequence.

Can an infinite arithmetic series ever converge?

An arithmetic series never converges: as \(n\) tends to infinity, the series will always tend to positive or negative infinity. Some geometric series converge (have a limit) and some diverge (as \(n\) tends to infinity, the series does not tend to any limit or it tends to infinity).