$$1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{2}{3}}}}}$$
In second term solving from the lowest part first denominator will be  $$\frac{5}{3}$$
second denominator will be $$\frac{8}{5}$$
third denominator will be $$\frac{13}{8}$$
fourth denominator will be $$\frac{13}{21}$$
hence eq. will reduce to 1+$$\frac{13}{21}$$ =Â $$\frac{34}{21}$$
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