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Homework Help: Showing that two sequences both converges to L

  1. Mar 17, 2010 #1
    1. The problem statement, all variables and given/known data

    Suppose that [tex]a_n \to L[/tex] and [tex]b_n \to L[/tex]. Show that the sequence[tex] a_1, b_2, a_2, b_2, a_3, b_3, ... [/tex]converges to L.

    2. Relevant equations

    3. The attempt at a solution

    I don't know.. how come [tex]b_2[/tex] is repeated? Do I need do use some kind of epsilon type proof?
  2. jcsd
  3. Mar 17, 2010 #2


    User Avatar

    It is probably a typo. Most likely it is supposed to be b1.

    Also, yes an epsilon argument will be most effective. Consider what it means for a sequence to converge. Then from the definitions you can obtain convergence of the new sequence.

    Hint: Use the max function.
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