HH_Sec_9_5

# HH_Sec_9_5 - R is 3 Example 4 What is the radius of...

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(9/1/08) Math 10B. Lecture Examples. Section 9.5. Power series and intervals of convergence Example 1 Find the radius of convergece of the power series s j =1 ( - 1) j +1 j x j = x - 1 2 x 2 + 1 3 x 3 - 1 4 x 4 + · · · . Answer: [Radius of convergence] = 1 (Figure A1a shows the partial sums for x = 0 . 75, where the series converges, and Figure A1b shows the partial sums for x = 1 . 2, where the series diverges.) N 10 20 y 1 ( x = 0 . 75) N 10 20 y 1 ( x = 1 . 2) y = N s n =1 ( - 1) n +1 n (0 . 75) n y = N s n =1 ( - 1) n +1 n (1 . 2) n Figure A1a Figure A1B Example 2 What is the radius of convergence of s n =0 1 (2 n )! x n ? Answer: The radius of convergence R is . Example 3 Find the radius of convergence of s n =1 x n n 3 3 n . Answer: The radius of convergence
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Unformatted text preview: R is 3. Example 4 What is the radius of convergence of ∞ s n =0 n ! x 2 n ? Answer: The radius of convergence R is 0. Interactive Examples Work the following Interactive Examples on Shenk’s web page, http//www.math.ucsd.edu/˜ashenk/: ‡ Section 10.7: Examples 1–4 † Lecture notes to accompany Section 9.5 of Calculus by Hughes-Hallett et al. ‡ The chapter and section numbers on Shenk’s web site refer to his calculus manuscript and not to the chapters and sections of the textbook for the course. 1...
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