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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 $A+B$ .