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GR-HMS 2013 Problem 1

    Let the sequence of real numbers (an),n=1,2,3...(a_n),n=1,2,3... with a1=2a_1=2 and an=(n+1n−1)(a1+a2+...+an−1),n≥2a_n=\left(\frac{n+1}{n-1} \right)\left(a_1+a_2+...+a_{n-1} \right),n\geq 2 . Find the term a2013a_{2013} .

    Dataset text AI-MO AoPS. Quoted with source.

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