Showing that two sequences both converges to L

  • Thread starter zeion
  • Start date
  • #1
467
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Homework Statement



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.


Homework Equations





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?
 

Answers and Replies

  • #2
jav
35
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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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