lp and c0 little question

Question

i want to explain that the inclusion $\bigcup_{p < \infty} l^p \subset c_0$ is true. that comes very quickly from the definition of $l^p$. The problem is, that Im sure that this inclusion is strict but I can't think on a counterexample. At this moment i think on something like $x_n = \frac{1}{\sqrt[p]{n} } $ but it doesn't seem to work. Any hint please?