# Infinite Fractions - 8

Algebra Level 3

$$\frac { 2+\frac { 2+\frac { 2+\cdots }{ { 2 }^{ 2 }+\cdots } }{ { 2 }^{ 2 }+\frac { 2+\cdots }{ { 2 }^{ 2 }+\cdots } } }{ { 2 }^{ 2 }+\frac { 2+\frac { 2+\cdots }{ { 2 }^{ 2 }+\cdots } }{ { 2 }^{ 2 }+\frac { 2+\cdots }{ { 2 }^{ 2 }+\cdots } } } =x$$

Given that $$x$$ is positive, find $$x$$.

Note: Round answer to $$3$$ decimal places.

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