Infinite Series

In this section we return to study a particular kind of sequence, those built by adding up more and more from a given collection of terms. One motivation comes from section 5.6, in which we obtained a sequence of approximating polynomials {P_n} to a given function. It is more natural to think of adding additional terms to the polynomial, and as such we are studying series. However, there is a closely related sequence; the sequence of partial sums.