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 $$\delta = \frac{d}{N}$$. The dielectric constant of the $$m^{th}$$ layer is $$K_m = K \left(1 + \frac {m}{N}\right)$$, For a very large $$N (> 10^3)$$, the capacitance C is $$\alpha \left(\frac{K \epsilon_0A}{d ln 2}\right)$$. The value of $$\alpha$$ will be _________.
[$$\epsilon_0$$ is the permittivity of free space]