** 28.T Sequences**

**NOTE: We will also be finishing up improper integrals on this
day.**

** Reference: ** Stewart 10.1

** Keywords: ** Infinite sequence, convergent sequence, divergent
sequence, limit of a sequence, monotonic sequence

** Learning Objectives: ** The student will be able to:

- Define what is meant by the limit of a sequence
- Determine whether a sequence converges or diverges
- Find the limit of a convergent sequence in simple cases

** 28.R Infinite series I **

** Reference:** Stewart 10.2, 10.3, 10.4

** Keywords: ** Series, infinite series,
sequence of partial sums, convergent series, divergent series,
geometric series, harmonic series, integral test, *p*-series,
estimates of series, comparison tests

** Learning Objectives:** The student will be able to:

- Define what is meant by the sum or limit of an infinite series
- Calculate partial sums of a series
- Recognize and find the sum of a geometric series
- Use limit laws to evaluate series
- Explain the analogy between series and improper integrals
- Use the integral test to determine whether a series converges or diverges
- Use improper integrals to obtain estimates for the sum of a series, or for the error of a partial sum
- Use the integral test to derive the
*p*-series test for convergence - Use the comparison and limit comparison tests for convergence