Chapter 11 Sequences and Series - San Dieguito …teachers.sduhsd.net/abrown/Classes/CalculusC/Chapter11.pdf · Chapter 11 Sequences and Series 11-1 Sequences 11-2 Series 11-3 Integral
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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
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!