Can I write $\prod_{i=1}^k$ if $k$ starts at 0?

Question

I'm hoping that $\prod_{i=1}^0i=1$.

Answer 1

Yes, it's called the empty product. The aim is to ensure $\prod_{i=1}^{n+1}a_i=a_{n+1}\prod_{i=1}^na_i$ still works when $n=0$. Similarly, an empty sum $\sum_{i=1}^0a_i=0$.