Answer
a) $\frac{R_1R_2}{R_1+R_2}$
b) $20/3\approx 6.7 ~\Omega$
Work Step by Step
a) $R=\frac{1}{\frac{1}{R_1}+\frac{1}{R_2}}=\frac{1}{\frac{R_2}{R_1R_2}+\frac{R_1}{R_1R_2}}=\frac{1}{\frac{R_1+R_2}{R_1R_2}}=\frac{R_1R_2}{R_1+R_2}$
b) Plugging in $R_1=10~\Omega,R_2=20~\Omega$, we get:
$R=\frac{10\cdot20}{10+20}=\frac{20}{3}~\Omega$
