Golden Geometric Progression

Algebra Level 2

2 ( 1 + x + x 2 + x 3 + ⋯ ) = 1 + 1 1 + 1 1 + 1 ⋱ \large 2(1+x+x^2+x^3+ \cdots) =1 + \cfrac 1{1+\cfrac 1{1+\cfrac 1{\ddots}}}

Real number x x as defined above is such that ∣ x ∣ < 1 |x| < 1 . Find x x ?

5 − 2 \sqrt { 5 }-2 1 − 2 1-\sqrt { 2 } 2 − 1 \sqrt { 2 }-1 2 − 5 2-\sqrt { 5 }

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Sanath Balaji by Sanath Balaji , 22, Singapore

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1 solution

Sanath Balaji
Dec 30, 2016

If you notice y is the Golden Ratio

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