A surd in the form of $\sqrt{a+\sqrt{a+\sqrt{a+...}}}$ is called an infinite surd, where \(a&

Question

A surd in the form of $\sqrt{a+\sqrt{a+\sqrt{a+...}}}$ is called an infinite surd, where $a>0$. Let $\operatorname{F}\left( a \right)=\sqrt{a+\sqrt{a+\sqrt{a+...}}}$. Evaluate $\operatorname{F}\left( 2 \right)$ and $\operatorname{F}\left( 6 \right)$. Simplify $\operatorname{F}\left( a \right)$, leaving your answer in terms of $a$.

Accepted Answer

(a) $F(2)=2,\ F(6)=3$ (b) $F(a)=\frac{1+\sqrt{1+4a}}2$

Surds - Infinite Nested Radicals

Surds - Infinite Nested Radicals

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