Definition:Convergent Product/Informal Definition
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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.