How will the signal $\sum_{n=-\infty}^\infty \Delta (t-n)u_{-1}(t-n)$ look like?
Initially, don't worry about the sum. Just try to figure out how the signal $\Delta(t)u_{-1}(t)$ looks like. As soon as you know that, you just need to shift it by integer values of $t$, and add them all up. If the shifted versions do not overlap, you simply get copies of the basic signal shifted to integer values of $t$. From the solution in the solution manual (as given in a comment), the basic signal is the right half of a triangle, and the period equals $1$. The symbol $u_{-1}(t)$ refers to the unit step function, which is more frequently referred to as $u(t)$ (see also this question and its answer(s)).