# Sampling of the DTFT causes the inverse transform to become periodic?

As you can see the above equation, DTFT is calculated from sample x[n] which is discrete sample of x(t).

But calculated X(w) is continuous, even though it is calculated from discrete value of x[n] as per equation 1.

How it is possible to get continuous output from discrete input??

What you may be missing is that $$\omega$$ is continuous. You can plug any value $$\omega \in \mathbb{R}$$ and get a number $$X_{2\pi}(\omega)$$. This is why $$X_{2\pi}$$ is continuous.
In this case, discrete and aperiodic time-domain signal $$x[n]$$ corresponds to a periodic and continuous frequency-domain signal $$X(\omega)$$.