Definition:Convergent Product/Informal Definition

Definition

A convergent product is an infinite (continued) product whose sequence of partial products converges.

Hence the phrase:

$\ds \prod_{n \mathop = 1}^\infty a_n$ diverges to $0$

then becomes:

$\ds \prod_{n \mathop = 1}^\infty a_n$ converges to $0$.

Also see

• Factors in Convergent Product Converge to One
• Convergence of Infinite Product Does not Depend on Finite Number of Factors
• Product of Convergent and Divergent Product is Divergent

which creates an analogy with series.

• Results about convergent products can be found here.