What is the precipitate of aqueous copper (II) and polysulfides?

So if you heat up a piece of sodium engulfed in a large excess of sulfur, what you would get (from what I've read) is sodium polysulfide $\ce{NaS\_n}$. But how large can $n$ get? If you left sodium polysulfide in molten sulfur, would you increase $n$?


If you tried to dissolve the sulfur-polysulfide mixture in water and filtered it, I assume you would get a basic aqueous hydrogen polysulfide solution. If you then poured in a solution of copper sulfate, besides $\ce{Cu(OH)2}$, would $\ce{CuS\_n}$ also precipitate out with an arbitrarily large $n$, or would the larger polysulfides break up into elemental sulfur and lower polysulfides first and precipitate out $\ce{CuS\_n}$ with a more discrete number $n$?


And if you acidified the polysulfide solution until you have only $\ce{HS-}$, $\ce{H2S}$ and suspended sulfur in the solution, from which you could get the precipitate $\ce{CuS}$, would you be able to calculate the initial mass of sodium used from the mass of copper sulfide?


