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Chapter 11Sequences and Series
11-1 Sequences11-2 Series11-3 Integral Test and p-Series11-4 Comparisons of Series11-5 Alternating Series11-6 Absolute Convergence
Ratio and Root Tests11-7 Clarifying the Confusion
Ten Tests for Series11-8 Power Series11-9 Representation of Functions as a Power Series11-11 Taylor Polynomials11-10 Taylor and Maclaurin SeriesReview
The following notes are for the Calculus C (SDSU Math 151)classes I teach at Torrey Pines High School. I wrote andmodified these notes over several semesters. Theexplanations are my own; however, I borrowed severalexamples and diagrams from the textbooks* my classes usedwhile I taught the course. Over time, I have changed someexamples and have forgotten which ones came from whichsources. Also, I have chosen to keep the notes in my ownhandwriting rather than type to maintain their informalityand to avoid the tedious task of typing so many formulas,equations, and diagrams. These notes are free for use by mycurrent and former students. If other calculus students andteachers find these notes useful, I would be happy to knowthat my work was helpful. - Abby Brown
SDUHSD
Abby Brown
Calculus II/CSDSU Math 151
www.abbymath.comSan Diego, CA
* , 6th & 4th editions, James Stewart, ©2007 & 1999Brooks/Cole Publishing Company, ISBN 0-495-01166-5 & 0-534-36298-2.(Chapter, section, page, and formula numbers refer to the 6th edition of this text.)
, 5th edition, Roland E. Larson, Robert P. Hostetler, & Bruce H. Edwards,
Calculus: Early Transcendentals
*Calculus ©1994D. C. Heath and Company, ISBN 0-669-35335-3.
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(Note: An error restriction of 1/1000 does not always mean you need 1000 terms, etc.)
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Abby Brown – Torrey Pines High School
1n
n
a
Infinite Series Tests for Convergence or Divergence
Test Converges Diverges Notes
nth-Term
Geometric 1
1
n
n
ar
Telescoping
Integral Test
p-Series 1
1p
n n
Direct Comparison
Limit Comparison
Alternating Series
Ratio Test
Root Test
What is the difference between absolute convergence and conditional convergence?
Sequences na What does it mean for a sequence to converge or diverge?
Don’t forget: 1
limn nn
n
a S
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This may not seem very interesting since it directly follows from the approximations we were working with before. However, it is important since it proves that if we let n approach infinity, then the series is EQUAL to f (x ) (in the interval of convergence) and not just an approximation!
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