Let F be a field. The set of all formal power series p(t) = a0 + a1t + a2t^2 + ..., with ai in F, forms a ring that is often denoted by F[[t]]. By formal power series, we mean that the coefficients form an arbitrary sequence of elements of F. There is no requirement of convergence. Prove that F[[t]] is a ring, and determine the units in this ring.