Series

(se'rēz.) [From L. sero, I plant.] Generally, a continued succe ion of things in the same order, and which are analogous with each other.-(Math.) A number of algebraic or arithmetical terms, increasing or decreasing in pursuance of a certain law. An arithmetical S. is one in which a common difference subsists between its consecutive terms. A harmonic S. has its every three sequent terms in harmonic al proportion. A geometrical S., one whose every term bears a constant ratio to the succeeding one, is a member of the group known as re currents. An infinite S. is a series comprising an infinite number of terms, at the end of which it is impo ible ever to arrive; so that, let the series be carried on to any a ignable length, or number of terms, it can be carried still further. [s. 815]