BC Calculus Assignments

Sequences and Series

EQ: How can we decide on the divergence or convergence of certain series?

College Board CalculusBC Standard

Sequence – Series – Converge – Diverges – Types of Tests

Day / Sec / Topic / Assignment / Key Idea
Mon
Mar 5 / 11.1 / Sequence
EQ: What is a sequence and does it converge or diverge? / Pg. 722: 1-51 odd, 73, 75 / Bounded
Monotonic
Converge-Diverge
Tues
½ Wed
Mar 67 / 11.2 / Series
EQ: What are the characteristics of a series and what are some of the ways we can tell if it converges or diverges? / Pg. 733: 15, 16,17, 19, 21, 22, 23, 25, 26, 27-45 odd,48, 57-63 odd, 79
Chart for tests / Infinite series
Converge-Diverge
Geom&Telescoping
Harmonic series
Divergence Test
½ Wed Mar 7 & Thurs
Mar 8 / 11.3
11.4 / The Integral and Comparison Test; Estimating Sums
EQ: How can the Integral Test and the Comparison Test show whether a series converges or diverges? / Review 11.1-11.4
Worksheet Practice 8.1-8.3 / Integral Test
Comparison Test
Limit Comp. Test
p-series
Fri
Mar 9 / 11.5
11.6 / Other convergence Tests
EQ: What other tests can help us tell whether a series converges or diverges? / Pg. 743: 9-27 odd, 28, 35
Take home Quiz
Begin Infinite Series Worksheet / Alternating Series
Alter. Ser Remainder
Absolute Converg.
Mon & Tues
Mar 12&13 / 11.5
11.6 / Other convergence Tests
EQ: What other tests can help us tell whether a series converges or diverges, especially series with negative terms? / Pg. 753: 3-13 odd, 23-27, 29
Pg. 759: 1, 3-29odd, 35, 37
Redo Pg. 743 #28 using absolute convergence
Mon: Infinite Series Wkst
Tues: Begin Series—Putting it all together / Ratio Test
Root Test
Wed
Mar 14 / Review / Cont.: Series—Putting it all together
Multiple Choice Seq & Series
Thurs
Mar15 / Test on Tests! / Review for Midterm! Monday Mar 19th

Even Answers: p. 733 #16) a) Same partial sum. b) the first series is an nth partial sum however the second series the sum of aj n times. 22) series is geometric with first term 10 and ratio

r = -10/9. Since absolute value of r is greater than 1, the series diverges. 26) Series is geometric with first term e and ratio r = e/3. Since absolute value of r is less than one, series converges. Sum is . 48)

Pg 743: 28) The function is not decreasing on [1, ∞) therefore we cannot use integral test. We will eventually be able to show this series converges absolutely and therefore converges.

Pg. 748: 2a) The series is divergent. 2b) we cannot say anything about .

Pg. 753: 24) Series converges by Alt. Series test. The sum has the required accuracy when we add the first four terms. 26) Series converges by Alt. Series Test. The sum has the required accuracy when we add the first 6 terms.