Summing Up Reciprocal of Central Binomial Coefficient

Calculus Level 5

n=11(2nn)\large \sum_{n=1}^\infty \frac{1}{{2n \choose n}}

Suppose the following infinite sum can be written as a+πbcd, \dfrac{a+\pi b\sqrt{c}}{d},

where a,b,ca,b,c and dd are integers with bb and cc prime. Then compute the value of a+b+c+da+b+c+d,

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