HH_Sec_9_3 - Math 10B Lecture Examples Section 9.3...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (9/7/08) Math 10B. Lecture Examples. Section 9.3. Convergence of series† ∞ Example 1 Does n=2 ∞ 1 n(ln n)2 1 = converge or diverge? 1 • The improper integral and the infinite series converge. (The first 24 partial ln(2) 2 sums of the series are plotted in Figure A1.) Answer: x(ln x)2 y 2 y = sN N sN = n=2 1 n(ln n) 2 1 Figure A1 10 ∞ 20 N Example 2 Does n=1 ∞ 1 √ converge or diverge? n 1 Answer: 1 √ x dx = ∞ • The infinite series diverges. (Its first 25 partial sums are plotted in Figure A2.) y y = sN 8 N sN = n=1 1 √ n 4 Figure A2 10 ∞ 20 N Example 3 Does n=1 ∞ ne−n converge? ∞ 2 2 2 Answer: 1 xe−x dx = ∞ 1 −1 e 2 • ne−n converges. n=1 Example 4 Does n=1 ∞ 1 n 1 1.75 converge or diverge? Answer: n=1 † Lecture n 1.75 converges. notes to accompany Section 9.3 of Calculus by Hughes-Hallett et al 1 Math 10B. Lecture Examples. (9/7/08) ∞ Section 9.3, p. 2 Example 5 Does n=1 ∞ n converge or diverge? n+1 Answer: n=1 n diverges. n+1 Interactive Examples Work the following Interactive Examples on Shenk’s web page, http//www.math.ucsd.edu/˜ashenk/:‡ Section 10.3: Examples 1–4 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. ‡ The ...
View Full Document

{[ snackBarMessage ]}

Page1 / 2

HH_Sec_9_3 - Math 10B Lecture Examples Section 9.3...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online