Does this summation require advanced techniques?

Calculus Level 4

Evaluate $\large \sum_{n=1}^{\infty}\dfrac{1}{\binom{2n}{n}}$

If the answer can be expressed as $$\dfrac{a+b\sqrt{c}\pi}{d}$$, where $$a,b,c$$ and $$d$$ are positive integers, $$c$$ is square-free, and $$d$$ is minimal, then find $$a+b+c+d$$.

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