Review of Series and Sequences - MATH 191[1]

Review of Series and Sequences - MATH 191[1] - SERIES...

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

SERIES - p -series Σ 1/ n p , convergent if p > 1, divergent if p 1. Geometric series Σ ar n -1 or Σ ar n , converges if | r | < 1, diverges when | r | 1 If the series has a form that is similar to a p -series or a geometric series, then one of the comparison tests should be considered. If Σ a n has some negative terms, then we can apply the Comparison Test to | Σ a n | and test for Absolute Convergence . If a n is of the form ( b n ) n , then the Root Test may be useful. If a n = f ( n ), where 1 ) ( dx x f is easily evaluated, then the Integral Test is effective (if hypotheses of test are satisfied) COMPARISON TESTS – Suppose that Σ a n and Σ b n are series with positive terms. Direct comparison test (a) if Σ b n is convergent and a n b n for all n, then Σ a n is also convergent. (b) if Σ b n is divergent and a n b n for all n, then Σ a n is also divergent. Limit comparison test (c) If 0 lim = c b a n n n , then either both series converge or both diverge.
Image of page 1

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

Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern