# 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.

## 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?