I came across the following property of the DTFT:
$ \mathcal{F} \Bigg(\sum_{m=- \infty}^{n}x[m]\Bigg) = \frac{1}{1- e^{-j \omega}} X(e^{-j \omega}) + \pi X(e^{-j0}) \sum_{m= -\infty}^{\infty}\delta({\omega- 2\pi k)}$
where capital X denotes the DTFT of the sequence x. I would really like to see how this is proved in a formal way as I cannot get there myself. Can anyone help me?