In this paper we investigate two problems concerning the theory of power series in eighteenth-century mathematics: the development of a given function into a power series and the converse problem, the return from a given power series to the function of which this power series is the development. The way of conceiving and solving these problems closely depended on the notion of function and in particular to the conception of a series as the result of a formal transformation of a function. After describing the procedures of the development considered acceptable by eighteenth-century mathematicians, we examine in detail the different strategies--both direct and converse, that is synthetic and analytical--they employed to solve these problems.