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Calculus Level 4

\[\sum _{ n=0 }^{ \infty }{ \frac { { \left( -\frac { { \pi }^{ 2 } }{ 4 } \right) }^{ n } }{ \left( 2n+1 \right) ! } } ={ \left( \frac { A }{ \pi } \right) }^{ B }\]

If the equation above holds true for integers \(A\) and \(B\), find the value of \(A+B\).

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