Logarithm of Divergent Product of Real Numbers
Jump to navigation
Jump to search
Theorem
Let $\left\langle{a_n}\right\rangle$ be a sequence of strictly positive real numbers.
Divergence to zero
The following are equivalent:
- The infinite product $\ds \prod_{n \mathop = 1}^\infty a_n$ diverges to $0$.
Divergence to infinity
The following statements are equivalent::
- $(1): \quad$ The infinite product $\ds \prod_{n \mathop = 1}^\infty a_n$ diverges to $+\infty$.
Also see
- Logarithm of Infinite Product of Real Numbers, for similar results