Cauch ' s form a ≤ ξ ≤ x This result holds if f(x) has continuous derivatives of order n at last. If lim R = 0 , the infinite series obtained is called n n →∞ Taylor series for f(x) about x = a. If a = 0 …

The geometric series has a special feature that makes it unlike a typical polynomial— the coefficients of the powers of x are the same, namely k. We will need to allow more general …

We begin by discussing the concept of a sequence. Intuitively, a sequence is an ordered list of objects or events. For instance, the sequence of events at a crime scene is important for …

(a) A sequence is an ordered list of numbers whereas a series is the sum of a list of numbers. (b) A series is convergent if the sequence of partial sums is a convergent sequence.

The rearrangement of a double series into a single series is one natural way to interpret a double series in terms of single series. Another way is to use iterated sums of single series.

Definition Series P ak converges () Sequence of Partial Sums fSng converges. Series P ak diverges () Sequence of Partial Sums fSng diverges. Using this definition to test a series for …

1. Convergence and Divergence Tests for Series ... 2. Important Series to Remember