Question: Accuracy of substitution

I have a question about the accuracy of Maple functions subs and evalf. I have some expressions such as the following: (more complicated). Let's call it f(n).  f(n) is not a polynomial in n or a rational function. It is a function of n involving exponents and four operations. When I plug in a large n in such an expression, would the answer I get (using evalf with some custom accuracy) be exact?  I am trying to prove f(n)/n >= constant. for ALL n.  If what I am trying to prove is true, then it must be that  f(n)/n should not get arbitrarily small no matter how large n is.   If I know that the numbers I get from f(n)/n is accurate for say, n=10^1000, then I can be confident that the claim is true.

Once again f(n) does not involve log, exp, sin etc. It only involves k'th roots of numbers and 4 operations.

Thanks a lot in advance.

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