Is there any way to evaluate this sum exactly?

$\displaystyle \frac{2}{3^1}+\frac{2}{3^2}+\frac{2}{3^6}+\frac{2} {3^{24}}+... = \sum_{n=1}^{\infty}\frac{2}{3^{n!}}$

If not, can someone give me a good approximation? Also, is there any way to know whether this is rational or irrational? How about algebraic or transcendental?