An arbitrary number of identical resistors in parallel

Uniting four resistors in parallel is equivalent to making a single resistor with the same length but four times the cross-sectional area. The result is to make a resistor with one quarter the resistance.

Question: What is the resistance of N identical resistors in parallel?

Solution: Generalizing the results for two and three resistors, we have

where "..." means that the sum includes all the resistors. If all the resistors are identical, this becomes