# Feeling Lucky?

Suppose you have a biased coin which comes up heads with probability $$\frac{1}{3}$$ and tails with probability $$\frac{2}{3}$$. You then begin to toss the coin repeatedly, with heads worth 1 point and tails worth 2 points, and add up the points as you go along.

Let $$p(n)$$ be the probability that at some stage you have accumulated precisely $$n$$ points. (For example, $$p(1) = \frac{1}{3}, p(2) = \frac{2}{3} + (\frac{1}{3})^{2} = \frac{7}{9}$$, etc..)

If $$\displaystyle\lim_{n\rightarrow \infty} p(n) = \dfrac{a}{b}$$, where $$a$$ and $$b$$ are positive coprime integers. Find $$a + b$$.

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