  We study the convergence of volume-normalized Betti numbers in
Benjamini-Schramm convergent sequences of non-positively curved manifolds with
finite volume. In particular, we show that if $X$ is an irreducible symmetric
space of noncompact type, $X \neq \mathbb H^3$, and $(M_n)$ is any
Benjamini-Schramm convergent sequence of finite volume $X$-manifolds, then the
normalized Betti numbers $b_k(M_n)/vol(M_n)$ converge for all $k$.
  As a corollary, if $X$ has higher rank and $(M_n)$ is any sequence of
distinct, finite volume $X$-manifolds, the normalized Betti numbers of $M_n$
converge to the $L^2$ Betti numbers of $X$. This extends our earlier work with
Nikolov, Raimbault and Samet, where we proved the same convergence result for
uniformly thick sequences of compact $X$-manifolds.
