Verify the formula for the total capacitance of a dielectric sandwich.

According to the hint we might be able to consider this as two capacitors in series. If we try this, we see

So, it looks like the assumption is correct. But, can we prove this assumption?

Yes. We can use Gauss's Law to show the electric fields inside our sandwich would be the same as two separate capacitors in series. Draw a gaussian box with the top surface inside the conductor and the bottom inside the top dielectric and you will see that you get the same electric field so therefore you get the same voltage across the whole sandwich.

OR: If you consider a very thin piece of conductor in between the layers of dielectric, you see you can stretch the conductor until it looks like the series capacitor.