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I was trying to work out why, so for two resistors, the calculation is:

R1.R2/(R1 + R2).

I thought of partial derivatives but not sure where to go after that, and after getting the curve in WolframAlpha, not sure what to do with that either.

http://www.wolframalpha.com/input/?i=plot+xy/(x+y)

Empirically, the nth case appears to be: min = (R1)/n and max = R1, but not sure how to prove it mathematically.

Any advice on what I could try next? This isn't homework, just noticed it and got curious.