How to calculate the DTFT of $1$? The sequence $x[n] = 1$ is not absolutely summable, so one can not compute the DTFT by using the definition
$$X(\Omega) \space = \sum \limits_{n=-\infty}^{\infty}x[n]e^{-j\Omega n}$$
Can anyone point me to a derivation of DTFT of $1$ from the first principles?
The derivations I came across used the fact that DTFT of $e^{j\Omega_0n}$ is
$$2\pi\sum \limits_{k=-\infty}^{\infty} \delta(\Omega-\Omega_0-2k\pi)$$
which again brings me to the question: how?