Closed form for $S_n = \sum_{i = 0}^n r^{n^i} = r + r^n + r^{n^2} + r^{n^3} + \cdots + r^{n^n}$?

Question

Find a closed form equation for the sum $$S_n = \sum_{i = 0}^n r^{n^i} = r + r^n + r^{n^2} + r^{n^3} + \cdots + r^{n^n}$$

I don't really think this is solvable. I tried with multiplying both side by something, and writing an terms of $S_n$ but it didn't help. Is it actually solvable?