Whilst trying to solve a combinatorics problem I am faced with summing this series:


1+ 2C\_1 2/(3^2) + 4C\_2 (2^2)/(3^4) + 6C\_3 (2^3)/(3^6)+ ... + 2nC\_n (2^n)/(3^(2n))+...


Where 4C\_2 is 4 choose 2.


Any idea how to approach this problem?



Trying to sum a series (related to catalan numbers perhaps)
The generating function of the [central binomial coefficients](http://en.wikipedia.org/wiki/Central_binomial_coefficient) is
$$\sum\_{n=0}^{\infty}\binom{2n}{n}x^n=\frac{1}{\sqrt{1-4x}}$$ and so the value of your series is 3.


