\(R_{78}=R_7+R_8=1+1=2\left(\text{Ω}\right)\)
\(R_{678}=\dfrac{R_6\cdot R_{78}}{R_6+R_{78}}=\dfrac{1\cdot2}{1+2}=\dfrac{2}{3}\left(\text{Ω}\right)\)
\(R_{5678}=R_5+R_{678}=1+\dfrac{2}{3}=\dfrac{5}{3}\left(\text{Ω}\right)\)
\(R_{45678}=\dfrac{R_4\cdot R_{5678}}{R_4+R_{5678}}=\dfrac{1\cdot\dfrac{5}{3}}{1+\dfrac{5}{3}}=\dfrac{5}{8}\left(\text{Ω}\right)\)
\(R_{345678}=R_3+R_{45678}=1+\dfrac{5}{8}=\dfrac{13}{8}\left(\text{Ω}\right)\)
\(R_{2345678}=\dfrac{R_2\cdot R_{345678}}{R_2+R_{345678}}=\dfrac{1\cdot\dfrac{13}{8}}{1+\dfrac{13}{8}}=\dfrac{13}{21}\left(\text{Ω}\right)\)
\(R_{AB}=R_1+R_{2345678}=1+\dfrac{13}{21}=\dfrac{34}{21}\left(\text{Ω}\right)\)
