Without using specific numerical values, explain why the equivalent resistance of any parallel arrangement of resistors is always less than the smallest individual resistance in that arrangement. Support your explanation with suitable algebraic reasoning for the case of two resistors R1 and R2 connected in parallel.
(a) Provide an algebraic explanation to show that the equivalent resistance of two resistors R1 and R2 connected in parallel is always less than each of R1 and R2.
(b) Using your reasoning, generalise the result for any number of resistors connected in parallel.