A note on the Taylor series remainder

Abstract

To solve the question of whether the remainder Rn of the Taylor series tends to zerowhen lim n = ∞, they try, as is known, to present the remainder in various forms, because often for this one form is more convenient than the other, as can be seen for example. at least in the log (1 + x) expansion. This method can obviously be generalized to find various forms of the remainder of interpolation formulas.