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 δ = d/N. The dielectric constant of the mᵗʰ layer is Kₘ = K(1 + m/N). For a very large N (>10³), the capacitance C is α(Kε₀A/(d ln 2)). The value of α will be ______. [ε₀ is the permittivity of free space]