132Lecture16.pdf

# 132Lecture16.pdf - Lecture 16 Midterm Review 1 Know the...

• Notes
• 3

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

Lecture 16: Midterm Review. 1. Know the difference between sequence convergence and series conver- gence. Series a n converges Sequence { a n } converges, and lim a n = 0 Series a n diverges Can’t tell sequence { a n } Sequence { a n } converges Can’t tell series a n Sequence { a n } diverges or converges but lim a n 6 = 0 Series a n diverges lim b n 6 = 0 Alternating Series ( - 1) n b n , ( - 1) n +1 b n diverges Example: If a n = ln( n ) n , the sequence converges as lim n →∞ a n = 0 by L’Hospital Rule; but series a n diverges by integral or comparison test. 2. p-test. 1 n p converges ⇐⇒ p > 1 R 1 1 x p dx converges ⇐⇒ p > 1 3. Geometric series n =1 ar n - 1 converges to a 1 - r ⇐⇒ r < 1 Example: Given n =1 ( x - 1) n 8 n - 1 , this is a geometric series with r = x - 1 8 , a = x - 1 , the series converges when | r | < 1, so - 7 < x < 9, and it converges to a 1 - r = x - 1 1 - x - 1 8 . 4. Alternating series test (must verify (two) conditions first, only apply to alternating series).

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

This is the end of the preview. Sign up to access the rest of the document.
• Summer '08
• WOLBACH
• Calculus, Mathematical Series, lim

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern