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Question Number 205941 by cortano12 last updated on 03/Apr/24

$$\:\:\:\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{2}}{\mathrm{3}}}}}}\:=?\: \\ $$$$\: \\ $$

Answered by mr W last updated on 03/Apr/24

2+(2/(2−(2/(2+(2/(2−(2/(2+(2/3))))))))) =2+(2/(2−(2/(2+(2/(2−(3/4))))))) =2+(2/(2−(2/(2+(8/5))))) =2+(2/(2−(5/9))) =2+((18)/(13)) =((44)/(13)) ✓

$$\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{2}}{\mathrm{3}}}}}} \\ $$$$=\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{3}}{\mathrm{4}}}}} \\ $$$$=\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{8}}{\mathrm{5}}}} \\ $$$$=\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{5}}{\mathrm{9}}} \\ $$$$=\mathrm{2}+\frac{\mathrm{18}}{\mathrm{13}} \\ $$$$=\frac{\mathrm{44}}{\mathrm{13}}\:\checkmark \\ $$

Commented by cortano12 last updated on 03/Apr/24

$$\:{not}\:\mathrm{3}\frac{\mathrm{5}}{\mathrm{13}}\:? \\ $$

Commented by Frix last updated on 03/Apr/24

3(5/(13))=3+(5/(13))=((39)/(13))+(5/(13))=((44)/(13))

$$\mathrm{3}\frac{\mathrm{5}}{\mathrm{13}}=\mathrm{3}+\frac{\mathrm{5}}{\mathrm{13}}=\frac{\mathrm{39}}{\mathrm{13}}+\frac{\mathrm{5}}{\mathrm{13}}=\frac{\mathrm{44}}{\mathrm{13}} \\ $$

Commented by cortano12 last updated on 03/Apr/24