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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?