Solution
= Solution
Write $v=(x+1)^l(x-1)^l$. In the <Leibniz rule> for its $l$th derivative at one, any term with fewer than $l$ derivatives on $(x-1)^l$ vanishes. The sole surviving term leaves $(x+1)^l$ undifferentiated and differentiates the second factor $l$ times, giving
$$
v^{(l)}(1)=2^l l!.
$$
The normalization in <Rodrigues' formula> consequently gives
$$
\boxed{P_l(1)=\frac{2^ll!}{2^ll!}=1.}
$$
The same argument covers $l=0$, with both zeroth powers equal to one.