Math 242: Principles of Analysis Fall 2016 Exam 2 Information . Department of Mathematics and Computer Science College of the Holy Cross

General Information

Important Definitions/Theorems/Axioms

• I will expect you to know how to use all of the definitions and theorems below to prove results similar to those on the homework assignments. You should know precise statements of the definitions and theorems in bold.
  • Definition 2.6.1 (Cauchy sequence)
  • Theorem 2.6.4
  • Definition of a contractive sequence.
  • Contractive sequences are Cauchy and therefore converge.
  • Definition 2.7.1 (infinite limits)
  • Theorem 2.7.5
  • Definition 6.1.1 (partial sums and convergence of a series)
  • Theorem 6.1.3
  • Theorem 6.1.5
  • The Cauchy Condensation Test
  • Theorem 6.1.7
  • Theorem 6.1.11
  • Corollary 6.1.12
  • Theorem 6.2.2
  • Corollary 6.2.3
  • Theorem 6.2.5
  • Theorem 6.2.9
  • The Root Test
  • Definition 6.3.1
• I will ask you to write a complete proof of one of (or one part of) the following theorems:
  • Theorem 2.6.4
  • Theorem 6.1.5
  • Theorem 6.1.11

Practice Questions