I have been having a difficult time writing $n!$ in capital $\prod$ notation.
Most of it is pretty easy but I can't seem to include $0!$ as a possible input since if I start the index $i$ at $0$, then the whole thing will be zero.
I have tried multiple other combinations of $i$ and $n$ but none of them have worked out. Any suggestions?
Best Answer
The empty product is by convention defined as one:
$$\prod_{i=1}^0 a_i = 1$$
Thus,
$$n! =\prod_{i=1}^n i$$