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Let (a_n)∞n=1 be a sequence defined recursively by a1 = 1, a_n+1 = sqrt(3a_n) for n...

Let (a_n)∞n=1 be a sequence defined recursively by a1 = 1, a_n+1 = sqrt(3a_n) for n ≥ 1. we know that the sequence converges. Find its limit.

Hint: You may make use of the property that lim n→∞ b_n = lim n→∞ b_n if a sequence (b_n)∞n=1 converges to a positive real number.  

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