Finding curcuit resistance

One of the advanced physics problems which had made an early impression on me, was to find a resistance of an n-steps ladder made out of identical resistors, and to solve this problem for an infinite steps ladder.
Solving of this problem in Mathematica makes it easy to deeper explore involved mathematical concepts, and these include continued fractions, algebraic numbers, recurrence equations to name a few. For instance, the resistance of an n-steps ladder is
Despite appearance of algebraic numbers in the answer, resistance is a rational number for every natural integer n. First few of these read 3 R, 11 R/4, 41 R/15 and so on.

The solution can be downloaded as a Mathematica Player notebook. One would need freely available Mathematica Player to view it and evaluate it. Enjoy!