Greek Sequence

Level pending

Let the sequence of real numbers \((a_n),n=1,2,3...\) with \(a_1=2\) and \(a_n=\left(\frac{n+1}{n-1} \right)\left(a_1+a_2+...+a_{n-1} \right),n\geq 2\). If the term \(a_{2014}\) can be expressed as \(2^ab\) , find the last three digits of \(a+b\).

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