The packing measure of the linear Gauss system

For every k ∈ N , let fₖ:[1/k+1, 1/k] → [0,1] be decreasing, linear functions such that fₖ(1/k+1) = 1 and fₖ(1/k) = 0 , k = 1, 2, . We define the iterated function system Sₙ by limiting the collection of functions fₖ to first n, meaning Sₙ = \{fₖ \}ₖ₌₁ⁿ . Let Jₙ denote the limit set of Sₙ . Then, limn→ ∞Ph_n(Jₙ) = 2 , where hₙ is the packing dimension of Jₙ and Ph_n is the corresponding packing measure.