A note on the remainder term of the Taylor series

Abstract

To determine whether the remainder Rn of the Taylor series tends to zero as lim n = ∞, it is common practice, as is well known, to represent the remainder in various forms. This is because, for this purpose, one form is often more convenient than another, as can be seen, for example, in the expansion of \( \log(1 + x) \). This method can obviously be generalized to find various forms of the remainder for interpolation formulas as well.

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