1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Series convergence

  1. Dec 1, 2009 #1


    User Avatar

    1. The problem statement, all variables and given/known data

    Show that if [tex]\sum[/tex]ak converges, then [tex]\sum[/tex] from k to ∞ of ak goes to zero as k goes to ∞.

    2. Relevant equations

    3. The attempt at a solution

    I'm not really sure how to go about this proof. But, this is my attempt,

    First I tried to show that [tex]\sum[/tex]ak is convergent.

    Let c be a real number and ε > 0. So there is an integer N > 0 such that if n > N then |an - c | < ε.

    So c is the limit of the sequence and an -> c.

    I don't really know where to go from there. Any help is appreciated.
  2. jcsd
  3. Dec 1, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    The definition of convergence of a series uses partial sums. What's the sum from k to infinity in terms of a partial sum?
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Series convergence
  1. Series Convergence (Replies: 3)

  2. Convergence of series (Replies: 2)

  3. Series convergence (Replies: 26)

  4. Convergence of a series (Replies: 24)

  5. Series Convergence (Replies: 15)