Solving the infinite resistor chain as a convergent sequence of sub-ladders

Solving the infinite resistor chain as a convergent sequence of sub-ladders

I knew that we can solve this famous physics puzzle by directly inferring a quadratic expression from the recursive structure of the resistors. Today in revising calculus I realized that I can also solve this puzzle by explicitly constructing a convergent sequence of "sub-ladders". I posted my solution just to share my small personal Eureka moment with my fellow physics enthusiasts!

submitted by /u/heartBreak1879
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