Multiplicative version of "summation"

Question

Repeated sum is denoted using $\sum$ and is called "summation." What is the name for the analogous process with multiplication, denoted $\prod$?

Answer 1

If there are finitely many terms to be multiplied, it is just called a product.

If $S(n)=\sum_{j=1}^n A_j$ and if $L=\lim_{n\to\infty} S(n)$ exists then we say $L=\sum_{j=1}^{\infty} A_j.$

Similarly if $P(n)=\prod_{j=1}^n B_j$ and if $M=\lim_{n\to\infty}P(n)$ exists then we write $M=\prod_{j=1}^{\infty} B_j.$ And we call $\prod_{j=1}^{\infty} B_j$ an infinite product.

There might be differing terminology in other languages. Jargon is not always translated verbatim.