Does this show that the Apery Constant is transcendental?
Solution 1:
No, because an infinite product of rationals is not necessarily rational.
For instance, $$\prod_{n=1}^\infty \left(1-\frac{1}{4n^2}\right)=\frac{2}{\pi}$$
is not rational.
Does this show that the Apery Constant is transcendental?
Solution 1:
No, because an infinite product of rationals is not necessarily rational.
For instance, $$\prod_{n=1}^\infty \left(1-\frac{1}{4n^2}\right)=\frac{2}{\pi}$$
is not rational.