What is the resistance when three resistors are connected in parallel, if the same connected in series has a resultant resistance of R?

We know that when two resistors a and b are connected in
series the equivalent resistance of the system is a +
b.

Now we are given that three resistors connected in
series give an equivalent resistance of R. Now this can be achieved using different
combinations, let’s take the simplest where the resistances of the three are equal, so
each resistor is of R/3 ohm.

When two resistors a and b are
connected in parallel the equivalent resistance is given as (1/a + 1/b) ^ (-1). So for
the three resistors connected in parallel the resistance is (1/(R/3) + 1/(R/3) +
1/(R/3)) ^-1 = (3 / (R/3)) ^-1 = R/9.

This value for
equivalent resistance is not constant but will change depending on the original
resistors we choose. For example, if we had taken R/2, R/4 and R/4 or any other similar
combinations, the result would have been different. The result given above is only one
example.