1. Section 8.1: Sequences

5. Definition Informal Definition Notation
A sequence is a function whose domain is ℕ.
Informal Definition
A sequence is a list.
Notation

6. Sequences s

7. Sequences s

10. Theorem
Suppose (sn ) converges to s and (tn ) converges to t.

15. Squeeze Theorem
Suppose and
Then

17. Tower of Power nn n! 3n en n4 n2 n √n ∜n
ln n

18. Examples
Diverges to infinity

19. Examples
Converges to 0

20. Examples
Converges to 0

21. Examples
Diverges to ∞

25. Important Facts to Know

26. Definitions is strictly increasing if for all n
is increasing if for all n
is strictly increasing if for all n
is decreasing if for all n
is strictly decreasing if for all n
is monotone if it is either increasing or decreasing

27. Definitions is bounded above by M if for all n
is bounded below by M if for all n
is bounded if it is bounded both above and below

28. Bounded Monotone Convergence Theorem
An increasing sequence converges if and only if it is bounded above.
A decreasing sequence converges if and only if it is bounded below.
A monotone sequence converges if and only if it is bounded.