# Resistors in infinite series

$\text{For} \space a > 1: \\ R = \tau (a) = \sum_{n=0}^{\infty} \frac{1}{a^n} = \frac{a}{a-1} \\ and \\ V = IR$

A circuit consisting of an infinite series of resistors is prepared such that the simplified equivalent resistor has a resistance ($$R$$) equal to $$\tau (a)$$. Determine the voltage ($$\text{V}$$) a circuit that has a resistance of $$\tau (5) \space Ω$$ and a current ($$\text{I}$$) of $$16 \space A$$.