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Question Number 184775 by SEKRET last updated on 11/Jan/23

(1/(6 + (9/(6 + ((25)/(6 + ((49)/(6 + ((81)/(6+ ......)) )) )) )) )) =?

$$\:\:\:\: \\ $$$$\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{6}\:+\:\frac{\mathrm{9}}{\mathrm{6}\:+\:\:\frac{\mathrm{25}}{\mathrm{6}\:\:+\:\:\frac{\mathrm{49}}{\mathrm{6}\:+\:\frac{\mathrm{81}}{\mathrm{6}+\:......}\:\:\:\:\:}\:\:\:\:\:}\:\:}\:\:\:\:\:\:\:\:}\:\:=? \\ $$$$ \\ $$$$ \\ $$

Commented by Frix last updated on 11/Jan/23

π−3?

$$\pi−\mathrm{3}? \\ $$

Commented by SEKRET last updated on 13/Jan/23

yes sir.provet that

$$\boldsymbol{\mathrm{yes}}\:\:\boldsymbol{\mathrm{sir}}.\boldsymbol{\mathrm{provet}}\:\boldsymbol{\mathrm{that}} \\ $$$$ \\ $$

Answered by aba last updated on 11/Jan/23

π=3+(1/(6+(3^2 /(6+(5^2 /(6+(7^2 /⋱_∞ ))))))) ⇒ (1/(6+(3^2 /(6+(5^2 /(6+(7^2 /⋱_∞ )))))))=π−3

$$\pi=\mathrm{3}+\frac{\mathrm{1}}{\mathrm{6}+\frac{\mathrm{3}^{\mathrm{2}} }{\mathrm{6}+\frac{\mathrm{5}^{\mathrm{2}} }{\mathrm{6}+\frac{\mathrm{7}^{\mathrm{2}} }{\ddots_{\infty} }}}}\:\Rightarrow\:\frac{\mathrm{1}}{\mathrm{6}+\frac{\mathrm{3}^{\mathrm{2}} }{\mathrm{6}+\frac{\mathrm{5}^{\mathrm{2}} }{\mathrm{6}+\frac{\mathrm{7}^{\mathrm{2}} }{\ddots_{\infty} }}}}=\pi−\mathrm{3} \\ $$

Commented by SEKRET last updated on 12/Jan/23

thank you sir. provet that

$$\boldsymbol{\mathrm{thank}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{sir}}. \\ $$$$\boldsymbol{\mathrm{provet}}\:\boldsymbol{\mathrm{that}} \\ $$

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