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 iterated function system (IFS) Sₙ by limiting the collection of functions fₖ to first n, meaning Sₙ = ₖ \ₖ₌₁ⁿ. Let Jₙ denote the limit set of Sₙ. Then limn→ ∞ Phₙ(Jₙ) = 2, where hₙ is the packing dimension of Jₙ and Phₙ is the corresponding packing measure.