# Series using mathematical induction

Algebra Level pending

A series $$\{a_n\}$$ has an initial starting value of $$a_1 =2$$. For all integers $$n$$, the two roots $$\alpha$$ and $$\beta$$ of the equation $$a_n x^2 - a_{n+1} x+1=0$$ satisfy the following condition: $\alpha - 2 \alpha \beta + \beta = 3.$ What is the minimum positive integer $$n$$ that satisfies $$a_n>1000?$$

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