AP CALCULUS BC
Section Number:
LECTURE NOTES
MR. RECORD
Day: 1 of 3
Topics: Power Series
- Power Series
- Radius and Interval of Convergence
9.8
Power Series
Goal: Show how an infinite polynomial functions can be used as an EXACT expression for other elem

Avon High School
AP Calculus BC
Name _
HW 9.1 Sequences
Period _
Write the first 5 terms of the sequence.
1.)
3.)
2n
an
n2
n
1 1
an (1) 2 2
n n
2.)
an cos n
4.)
an
2n !
n 1 !
Write an expression for the nth term of the sequence.
5.)
7.)
1, 5, 9, 13, K

Avon High School
AP Calculus BC
Name _
HW 9.3 The Integral Test and p-Series
Period _
Score _ / 10
In the following exercises, use the Integral Test to determine the convergence or divergence of the series. Be
sure to properly justify your conclusion.
1.)

Avon High School
AP Calculus BC
Name _
HW 9.4 Comparison of Series
Period _
Score _ / 10
Use the Direct Comparison Test to determine the convergence or divergence of each of the following series.
1.)
3.)
5.)
1
n2 2
n 1
1
n3
n4
1
4n 1
n 5
2.)
3n
n 1
4.

AP CALCULUS BC
Section Number:
9.3
LECTURE NOTES
Topics: The Integral Test and p-Series
- The Integral Test
- p-Series and The Harmonic Series
MR. RECORD
Day: 1 of 1
The Integral Test
THEOREM 9.10: THE INTEGRAL TEST
If f is positive, continuous, and decre

AP CALCULUS BC
Section Number:
LECTURE NOTES
Topics: Series and Convergence
- Infinite Series
- Geometric Series
9.2
MR. RECORD
Day: 1 of 2
Infinite Series
Series:
`
a
n 1
n
Sequence of Partial Sums:
a1 a2 a3 L an L
S1 a1
S 2 a1 a2
S3 a1 a2 a3
M
S n a1 a

AP CALCULUS BC
Section Number:
LECTURE NOTES
Topics: Comparison of Series
- Direct Comparison Test
- Limit Comparison Test
9.4
MR. RECORD
Day: 1 of 1
Direct Comparison Test
For the convergence tests that we have discussed so far, the terms of the series s

AP CALCULUS BC
Section Number:
9.9
LECTURE NOTES
Topics: Representations of Functions by Power Series
- Geometric Power Series
- Operations with Power Series (Adding)
MR. RECORD
Day: 1 of 2
Geometric Power Series
Goal: Investigate techniques for finding a

AP CALCULUS BC
Section Number:
LECTURE NOTES
Topics: Taylor Polynomials and Approximations
- Taylor Polynomials
- Maclaurin Polynomials
9.7
MR. RECORD
Day: 1 of 3
Polynomial Approximations of Elementary Functions
Goal: Show how polynomial functions can be

`AP CALCULUS BC
Section Number:
9.10
LECTURE NOTES
Topics: Taylor and Maclaurin Series
- Taylor and Maclaurin Series
Taylor and Maclaurin Series
THEOREM 9.22
THE FORM OF A CONVERGENCT POWER SERIES
If f is represented by a power series
for all x in an open

AP CALCULUS BC
Section Number:
LECTURE NOTES
Topics: Alternating Series
- Alternating Series
- Alternating Series Remainder
9.5
MR. RECORD
Day: 1 of 2
Alternating Series
Up to now, most series we have dealt with had positive terms. In this section and bey

AP CALCULUS BC
Section Number:
9.6
LECTURE NOTES
Topics: The Ratio and Root Tests
- The Ratio Test
MR. RECORD
Day: 1 of 2
The Ratio Test
Here is another test for absolute convergence the Ratio Test.
THEOREM 9.17: RATIO TEST
Let
1.
an
an
be a series with

Avon High School
AP Calculus BC
Name _
HW 9.2 Series and Convergence
Period _
Score _ / 10
In the following exercises, find the sum of the convergent series. Be sure to properly justify your conclusion.
1.)
1
3
n 0
3.)
n 0
5.)
2.)
n
1
2
4
2 5
n 0