9-1 SequencesObjective: Determine whether a sequence

converges or diverges and use properties of monotonic sequences and bounded sequences.

Ms. BattagliaAP Calculus

a) The terms of the sequence {an} = {3 + (-1)n} are

b) The terms of the sequence {bn} = are

Listing the Terms of a Sequence

c) The terms of the sequence {cn} = are

d) The terms of the recursively defined sequence {dn}, where d1 = 25 and dn+1 = dn - 5

Listing the Terms of a Sequence

Find the limit of the sequence whose nth term is

Finding the Limit of a Sequence

a) {an} = {3 + (-1)n} b) {bn} =

Determining Converges or Divergence

Show that the sequence whose nth term is

convergence.

Using L’Hôpital’s Rule to Determine Convergence

Show that the sequence converges, and find its limit.

Using the Squeeze Theorem

Find a sequence {an} whose first five terms are

Finding the nth term of a Sequence

Determine an nth term for a sequence whose first five terms are

Finding the nth Term of a Sequence

Determine whether each sequence having the given nth term is monotonic.

a) b) c)

Determining Whether a Sequence is Monotonic

a. {an} = {1/n} b. {bn} = {n2/(n+1)} c. {cn}={(-1)n}

Bounded and Monotonic Sequences

Day 1: Read 9.1 Page 604 #45-51 odd, 85-95 odd

Day 2: Page 604 #55-67 odd, 88-99 even, 119-124

Classwork/Homework