Sequences and series (6)

Algebra Level 3

A sequence of positive terms \(A_{1}, A_{2}, A_{3}, \cdots, A_{n}\) satisfies the relation \( A_{n+1} = \dfrac{3(1+A_{n})}{(3+A_{n})}\). Find the least integral value of \(A_{1}\) for which the above sequence is decreasing.

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