Exercise 4.8.1.6. Let $n$ be a positive integer and let $\operatorname{\mathcal{C}}$ be a differential graded category which satisfies the following condition:
For every pair of objects $X,Y \in \operatorname{\mathcal{C}}$, the chain complex $\operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y)_{\ast }$ is concentrated in degrees $< n$: that is, the abelian groups $\operatorname{Hom}_{\operatorname{\mathcal{C}}}(X,Y)_{m}$ vanish for $m \geq n$.
Show that the differential graded nerve $\operatorname{N}_{\bullet }^{\operatorname{dg}}(\operatorname{\mathcal{C}})$ is an $(n,1)$-category (see the proof of Theorem 2.5.3.10).