Calculating output voltage of a boost converter circuit
The switch is shorted from t = 0 to T0, then opened until T1 with
i(T0+T1) = 0. This operation is repeated n times.

You are operating at the boundary condition (and you need an appropriate load for this to remain so). Try reading this on the link I gave earlier: -


Calculating output voltage of a boost converter circuit

$$V_{OUT} = V_{IN}\cdot \dfrac{1}{1-D}$$
This requires that the output load be appropriately sized i.e. it perfectly consumes all the power supplied by the inductor in each switching cycle.