Showing that two sequences both converges to L

[zeion]

Homework Statement

Suppose that $$a_n \to L$$ and $$b_n \to L$$. Show that the sequence$$a_1, b_2, a_2, b_2, a_3, b_3, ...$$converges to L.

Homework Equations

The Attempt at a Solution

I don't know.. how come $$b_2$$ is repeated? Do I need do use some kind of epsilon type proof?

 

[jav]

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.