> Let alpha = 0.110001000000000000000001000..., where the 1's occur in the n! place, for each n. Then alpha is transcendental. (Calculus, 4th edition by Michael Spivak)
Nearly all infinite sums involving factorial are transcendental.
However, only a small proportion of people who know what "transcendental" means are capable of proving that any number is transcendental.
> Let alpha = 0.110001000000000000000001000..., where the 1's occur in the n! place, for each n. Then alpha is transcendental. (Calculus, 4th edition by Michael Spivak)
Nearly all infinite sums involving factorial are transcendental.