It should be in Combinatorics section

Calculus Level 5

$\large \displaystyle \lim _{ n\rightarrow \infty }{ \sum _{ r=1 }^{ n }{ \frac { ^{ 2r }{ { C }_{ r } } }{ { 2 }^{ 2r }\left( 2r+1 \right) } } } = \frac { \pi }{ a } -b$

If the series above is true for constants $$a,b$$, find the value of $$a+b$$.

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