# Square Roots Of Sequences

Algebra Level 4

Let $$(a_n)_{n=1}^{\infty}$$ be a sequence of positive real numbers such that for $$n \ge 1$$ we have $$a_{n+2} = \sqrt{a_{n+1}}+\sqrt{a_n}$$.

Find $$\displaystyle\lim_{n\to\infty} a_n$$.

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