I have trouble understanding the proof I was provided of the IDFT, here is what I have: $$ \nu_n = \frac{n}{\Delta N} \\ x(t) = \int_{-\infty}^{\infty}X(\nu)e^{i2\pi\nu_n t}d\nu \\ $$
the next step I have is the troublesome one:
$$ x(k\Delta) = \sum_{n = 0}^{N - 1} \Delta X_k e^{\frac{i2\pi n k\Delta}{\Delta N}} \frac{1}{\Delta N} $$
It is obvious where some of the elements are canceling each other, but I do not understand how the $ \frac{1}{\Delta N}$ is at the end? Do we get it when we convert $d\nu$?
Thank you a lot!