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GAIC Math 2024 Problem 52

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Given the sequence {an}:a1=1,an+1=3an+13−an\{a_n\}: a_1=1, a_{n+1}=\frac{\sqrt{3}a_n+1}{\sqrt{3}-a_n}, then ∑n=12022an=_____\sum\limits_{n=1}^{2022}a_n=\_\_\_\_\_.

Dataset text MathOdyssey. Open licence.

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