Is 1/product(k)=product(1/k)?

Question

I'm wondering: The common product operator is denoted as $ \Pi z_k $ which is simply $z_1*z_2*z_3...z^n$. If you reciprocated that product, it would be $ \frac{1}{ \Pi z_k}$ which is $ \frac{1}{z_1*z_2*z_3...} $. However, that seems like it could be notated as $ \Pi \frac{1}{z_k} $. Is that true? I don't see how it wouldn't be but I've never seen that before.

Answer 1

Yes, that's right. It's the multiplicative analogy of the fact that when summing, $-\sum a_k = \sum (-a_k)$.