Question Number 149423 by mathdanisur last updated on 05/Aug/21

((2207 - (1/(2207 - (1/(2207 - ...))))))^(1/8) = ?

Answered by dumitrel last updated on 05/Aug/21

x=2207−(1/(2207−(1/(2207−....))))⇒x=2207−(1/x)⇒x=((2207+21∙47(√5))/2) (((1+(√5))/2))^(16) =...=((2^(15) (2207+21∙47(√5)))/2^(16) )=x⇒(((((1+(√5))/2))^(16) ))^(1/8) =(((1+(√5))/2))^2 =((3+(√5))/2)

Commented bymathdanisur last updated on 05/Aug/21

Thank You Ser, Cool