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Algebra Level 3

1 + 1 + 1 + . . . ∞ \sqrt{1+\sqrt{1+\sqrt{1+...\infty}}} = X =X

Find X X upto 3 decimal


The answer is 1.618.

Moaj Ahmed by Moaj Ahmed , 25, Bangladesh

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1 solution

X = 1 + 1 + 1 + . . . ∞ X = \sqrt{1 + \sqrt{1 + \sqrt{ 1 + . . . \infty}}}

X 2 = 1 + 1 + 1 + 1 + . . . ∞ X^2 = 1 + \sqrt{1 + \sqrt{1 + \sqrt{ 1 + . . . \infty}}}

X 2 = 1 + X X^2 = 1 + X

X 2 − X − 1 = 0 X^2 - X - 1 = 0

X = 1 + 5 2 = 1.618 X = \frac{1 + \sqrt{5}}{2} = \boxed{1.618}

5 Helpful 0 Interesting 0 Brilliant 0 Confused

Or ϕ \phi the Golden ratio.

Seth Lovelace - 6 years, 4 months ago

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