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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