Deriving epsilon with a context free grammar with epsilon rules
Here's an example to get you started. Suppose our grammar had productions
$$
S\rightarrow TT\qquad T\rightarrow UU\qquad U\rightarrow \epsilon
$$
so $l=2, m=3$.

Then, how fast can you get from $S$ to $\epsilon$? Clearly, it'll take 7 steps:
$$
S\Rightarrow TT\Rightarrow UUT\Rightarrow UUUU\Rightarrow UUU\Rightarrow UU\Rightarrow U\Rightarrow \epsilon
$$
Notice that $(l^m-1)/(l-1)=(2^3-1)/(2-1)=7$.

What does the parse tree for this derivation look like? In particular, how many leaves will it have?

Now generalize this construction.