In this paper it is shown that if c is a point of the region of convergence of an analytic function f(z) = Σ∞ncnZn then in every neighborhood of c there exists a point e such that the value f(c) of the function f(z) is attained by some truncation Σkn=0cnZn off(z) at z = e, i.e., Σkn=0cnen = Σ∞n=0cncn. Also it is shown that the above does not hold in the case of real-valued functions of a real variable.