Our topic is the convergence of one class of the series of rational operators in the field $M$ of Mikushiński operators. Using Ditkin's result [2] which connects the operators with Laplace transformations and following the ideas of Erdelyi, [3] we will give the representation in the field $M$ of the following convergent series of rational operators \[ \Big(1+\frac x{ks+p-x}\Big)^v=um_{n=0}^{ıfty}\frac{(v)_nx^n}{n!(ks+p)^n}\qquad(Rev>0) \] \emph{where $p$ is an arbitrary complex number and $k>0$}.