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