Considering for each n $$\in \mathbb{N}$$, the improper integral f(x) = $$\int_{0}^{\infty} (t^(n-1)/e^t - 1) dt $$ regarding f(2k), we can state that
a) If the integral converges, then f(2k) isn't limited regarding K
b)If the integral converges, then f(2k) squared is rational
c)If the integral converges, f(2k) is rational.
d)It diverges for every k $\in $\mathbb{N}