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Moldova NMO, 11th grade, Day 2, Problem 6

Source: Easy .. still, to post the complete olympiad...

March 4, 2007
algebra unsolvedalgebra

Problem Statement

Define (bn)(b_{n}) to be: b0=12b_{0}=12, b1=32b_{1}=\frac{\sqrt{3}}{2} adn bn+1+bn−1=bn⋅3b_{n+1}+b_{n-1}=b_{n}\cdot\sqrt{3}. Find b0+b1+⋯+b2007b_{0}+b_{1}+\dots+b_{2007}. Note. Maybe this seems too easy, but I want to post all the problems...
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