Question: Request for advice on recursion

According to the attached file "test" I would like to determine the limit of the function f(n,x) for n-->00 as an exercise. I'm asking for advice on using "rsolve". I also want to calculate the limit of sqrt((n/3))*f(n,x) for n-->00 using f(n,x) from the file "test". I also need help with this. (This isn't a school assignment ;-).)

test.mw

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