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Question Number 61625 by Sharath Kumar last updated on 05/Jun/19
1+(1/(1+(1/(1+(1/(1+(1/(1+(1/(1+...))))))))))=
$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}+…}}}}}= \\ $$
Answered by MJS last updated on 05/Jun/19
x=1+(1/x) ∧ x>1 ⇒ x=(1/2)+((√5)/2)
$${x}=\mathrm{1}+\frac{\mathrm{1}}{{x}}\:\wedge\:{x}>\mathrm{1}\:\Rightarrow\:{x}=\frac{\mathrm{1}}{\mathrm{2}}+\frac{\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$
Commented by Kunal12588 last updated on 05/Jun/19
(((√5)+1)/2)=1.61803398.....      isn′t it Golden Ratio.
$$\frac{\sqrt{\mathrm{5}}+\mathrm{1}}{\mathrm{2}}=\mathrm{1}.\mathrm{61803398}…..\:\:\:\:\:\:{isn}'{t}\:{it}\:{Golden}\:{Ratio}. \\ $$
Commented by MJS last updated on 06/Jun/19
yes
$$\mathrm{yes} \\ $$

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