Give an example of a sequence of functions $f\_{n} \in L\_{1}(\mathbb{R}) \cap L\_{2}(\mathbb{R})$ for $n=1,2,3,....$ such that $\frac{||f\_n||\_1}{||f\_n||\_2} \rightarrow 0$.

**Thoughts** I can find functions such that $\frac{||f\_n||\_2}{||f\_n||\_1} \rightarrow 0$ but any sequence of functions I can think of that tend to zero in $L\_{2}$ either tend to zero in $L\_{1}$ aswell or aren't in $L\_{1}$ at all.