JEE Advanced 2019 · Paper 1, Physics question 16

A parallel plate capacitor of capacitance $C$ has spacing $d$ between two plates having area $A$. The region between the plates is filled with $N$ dielectric layers, parallel to its plates, each with thickness $\delta = \dfrac dN$. The dielectric constant of the $m^{th}$ layer is $K_m = K\left(1 + \dfrac mN\right)$. For a very large $N\ (> 10^3)$, the capacitance $C$ is $\alpha\left(\dfrac{K\epsilon_0A}{d\ln2}\right)$. The value of $\alpha$ will be ______.

[$\epsilon_0$ is the permittivity of free space]