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, $\delta = {d \over N}$. The dielectric constant of the mth layer is $${K_m} = K\left( {1 + {m \over N}} \right)$$. For a very large N(>103), the capacitance C is $$\alpha \left( {{{K{\varepsilon _0}A} \over {d\ln 2}}} \right)$$ The value of $\alpha$ will be .................. [$\in$ 0 is the permittivity of free space.]