Power series. Derivative of a power series, integral of a power series. Exercises скачать в хорошем качестве

Power series. Derivative of a power series, integral of a power series. Exercises

How does the derivative and integral of a power series behave. After having seen the concept of a power series, determining the radius of convergence and the interval of convergence, we propose to derive all the infinite terms of a series of functions. Will the new series still be a power series in any case? If so, will it have the same radius of convergence as the original series? Will it have the same set of convergence as the original series? The same considerations will also be made for the operation of integration by series. Some examples will clarify the concepts explained and thanks to one of these exercises we will discover the sum of a particular numerical series seen in the playlist dedicated to numerical series: we are referring to the harmonic series with terms of alternating sign of which we know its character (convergent), but we do not know the real number to which it converges. The exercise will clarify all the ideas. #salvoromeo #seriepotenze #derivazioneperserie