Question-65753

Question Number 65753 by Masumsiddiqui399@gmail.com last updated on 03/Aug/19

Answered by mr W last updated on 04/Aug/19

1^{*)}

\sqrt{1 + 1}

\sqrt{\sqrt{1 + 1} + 1}

\sqrt{\sqrt{\sqrt{1 + 1} + 1} + 1}

\sqrt{\sqrt{\sqrt{\sqrt{1 + 1} + 1} + 1} + 1}

\dots \dots

\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{\sqrt{1 + 1} + 1} + 1} + 1} + 1} + 1 \dots .} = x

x^{2} - 1 = x

\Rightarrow x^{2} - x - 1 = 0

\Rightarrow x = \frac{1 + \sqrt{5}}{2} = φ = g o l d e n r a t i o \approx 1.618

^{*)} a c t u a l l y y o u m u s t n o t s t a r t w i t h

“ 1^{″}, y o u c a n s t a r t w i t h a n y n u m b e r,

t h e f i n a l r e s u l t i s a l w a y s t h e s a m e .

Commented by mr W last updated on 03/Aug/19

i t r i e d w i t h m y c a l c u l a t o r, i g o t

a f t e r a f e w s t e p s f o l l o w i n g r e s u l t

Commented by mr W last updated on 03/Aug/19

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