Counting measure and inclusion of $\mathcal{L}_p$ spaces.

Question

Let $(X,\mu,\mathfrak{A})$ be a measure space with the counting measure such that X is countably infinite or finite. Let $1\leq p_1 < p_2 < \infty$ I just showed that $\mathcal{L}_{p_1} \subset \mathcal{L}_{p_2}$ but I am also asked to show that the inclusion is strict if X is infinite but I don't really know how to do this. I know that I am looking for a function such that $\sum\limits_{i=1}^\infty |f(x_i)|^{p_2}$ converges but $\sum\limits_{i=1}^\infty |f(x_i)|^{p_1}$ doesn't but I can't think of one.