Answer
True.
Work Step by Step
See p.267, text following the definition of Riemann sums.
...For a general partition, the norm is related to the number of subintervals of $[a, b]$ in the following way:
$\displaystyle \frac{b-a}{\Vert\Delta\Vert}\leq n$
So, the number of subintervals in a partition approaches infinity as the norm of the
partition approaches $0$.
The statement is true.