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 \(a+b\).

This question is part of set Serieses are fun!.
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