Series with fractional number of terms

Abstract

Series of numbers with fractional number of terms have generally no meaning and so they are not treated in modern works on algebra. But such series are found to occur in ancient Indian works on arithmetic, where they have been assigned a geometrical or symbolical significance. Originally such series were interpreted with the help of figures resembling a ladder or a drinking glass, but in course of time an analytical meaning was also given to them. In doing so the Indian mathematicians were guided by certain problems that arose in everyday life. In this brief note we shall put forward the Indian stand-point with reference to arithmetic series having fractional number of terms.