Chapter 11 on infinite series and sequences is very different from the earlier material. It is much more theoretical. It is almost like we are starting a new course. It involves a very different way of thinking. You may need to double or triple your study time before you "get it."

The text does not have many applications. This can make it hard for some students to stay motivated. I'll try to do some applications in class, but, be forewarned, the applications can be messy in themselves.

The numbers in brackets refer to the numbers inside the red boxes in your textbook.

• Section 11.1
  • [1] Understand way this definition is too vague.
  • [2] Correct Definition: know & understand.
  • [3] Theorem: Know this easy fact.
  • [4] Know this.
  • [5] Definition: Know & understand.
  • (page 705) Limit Laws for Sequences: Know these; be able to prove the first and third.
  • (page 705) Squeeze Theorem for Sequences: Know & understand.
  • [6] Theorem: Know & be able to prove.
  • [8] (Theorem): Know and be able to prove.
  • [9] Definition: Know & understand.
  • [10] Definition: Know & understand.
  • [11] Monotone Sequence Theorem: Know and understand pictorially.
• Section 11.2
  • [2] Definition: Know & understand.
  • [4] (Theorem): Know and be able to prove!
  • [5] A useful special case of [4].
  • [6] Theorem: Know and understand intuitively.
  • [7] The Test for Divergence: Know & understand.
  • [8] Theorem: Know and be able to prove (i) & (ii).
• Section 11.3
  • (page 724) The Integral Test: Know & understand pictorially.
  • [1] (p-series theorem): Know and be able to prove using Integral Test.
  • [2] Remainder Estimate for the Integral Test: Know & be able to use.
• Section 11.4
  • (page 731) The Comparison Test: Know and be able to prove.
  • (page 732) The Limit Comparison Test: Know & try to understand pictorially.
• Section 11.5
  • (page 736) The Alternating Series Test: Know & try to understand pictorially.
  • (page 738) Alternating Series Estimation Theorem: Know.
• Section 11.6
  • [1] Definition: Know & understand.
  • [2] Definition: Know & understand.
  • [3] Theorem: Know and be able to prove.
  • (page 742) The Ratio Test: Know & be able use.
  • (page 744) The Root Test: Know & be able to use.
• Section 11.7
  • Nothing new here.
• Section 11.8
  • [1] & [2]: Know these definitions.
  • [3] Theorem: Know this.
• Section 11.9
  • [2] Theorem: Know this simple theorem. (It looks messy, but is not.)
• Section 11.10
  • [5] & [6] are the same: They are of fundamental importance!
  • [7]: a useful special case of [6].
  • [8] Theorem: a minor factoid.
  • [9] Taylor's Inequality (usually called Taylor's Remainder Theorem): Know this and be able to use it.
  • [11] Know the this!! ([12] is the same thing.)
  • [15] Know this!
  • [16] Know this!
  • Ask me why e^it = cos(t)+i*sin(t).
  • Know the table on the bottom of page 767.
• Section 11.11
  • [2] The Binomial Series: Know & be able to use.
• Section 11.12
  • No more theorems!