ABSTRACT
We have seen that finite Riemann sums can be used to approximate definite integrals. However, they do just that-approximate. In order to obtain the exact result, we need the limits of these sums. Similarly, Taylor polynomials provide approximations of functions, but there is the error term rn. Remark 4.5.4 reminds us that, as n → ∞, this error goes to 0, which means that we would have an exact equality between the function and the Taylor polynomial if the latter had infinitely many terms. Such sums (with infinitely many terms) are the infinite series and they will be the focus of our study in this chapter.
