Week 28

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