Min and Max of Parallel Resistors

[meeep]

I noticed that, for resistors in a parallel circuit, where R1 is < R2, the minimum value is (R1)/2, and the maximum approaches R1.
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.

 

[Office_Shredder]

Assume that R₁ is some fixed number. All that we know is that R₂ must be bigger than R₁. So to find the minimum resistance, R₂ should be as small as possible, and to find the maximum resistance, R₂ should be infinitely large.

Try seeing what happens to the resistance when you make R₂ as small as possible (keeping in mind it must be bigger than R₁) and what happens when R₂ is arbitrarily large