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Series convergence

  1. Dec 1, 2009 #1

    hth

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    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

    Dick

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    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?
     
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