{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Notes on Series - Continued

Notes on Series - Continued - Notes on Series Continued...

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

View Full Document Right Arrow Icon
Notes on Series - Continued Convergent series may be thought of as finite sums as they ‘sum’ to a finite number. Therefore we can have an arithmetic associated with them. Divergent series though do not have arithmetical properties. Convergent series may be multiplied by a constant number, added together, subtracted from each other, multiplied together and divided. In this course we only consider the first three arithmetic operations though. The theorem below provides the relevant statements. Theorem : A) Suppose n a and n b are convergent series and c is a constant. Then the series n ca and ( 29 n n a b ± are all convergent series, and n n ca c a = ( 29 n n n n a b a b ± = ± B) Suppose n a diverges and c is a constant. Then n ca diverges for 0 c , and, if n b is a convergent series, then ( 29 n n a b ± diverges. Examples : Below are some examples of how this theorem may be used to determine convergence/divergence of certain series. 1) Show the series 1 1 1 1 2 2 3 n n n + - = - converges and find the sum of the series.
Image of page 1

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

View Full Document Right Arrow Icon
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