Infinite product 无穷乘积
In mathematics, for a sequence of complex numbers a1, a2, a3, ... the infinite product
is defined to be the limit of the partial products a1a2...an as n increases without bound. The product is said to converge when the limit exists and is not zero. Otherwise the product is said to diverge. A limit of zero is treated specially in order to obtain results analogous to those for infinite sums. Some sources allow convergence to 0 if there are only a finite number of zero factors and the product of the non-zero factors is non-zero, but for simplicity we will not allow that here. If the product converges, then the limit of the sequence an as n increases without bound must be 1, while the converse is in general not true.
![\prod_{n=1}^{\infty} a_n = a_1 \; a_2 \; a_3 \cdots](/Images/godic/202501/20/99ae7470923d203d9fa8ab14468c457d1425.png")