# What's gamma doing inside?

Calculus Level 5

$\large \displaystyle \sum _{ k=1 }^{ \infty }{ \dfrac { { \left( -1 \right) }^{ k } }{ k\Gamma \left( k+1 \right) \left[ \left( -\dfrac { 2k+1 }{ 2 } \right) ! \right] } }$

If the value of the series above is in the form of

$\dfrac C{\pi^{A/B} } \ln D,$

where $$A,B,C$$ and $$D$$ are positive integers with $$D$$ is a not a perfect power and $$A,B$$ coprime, find $$A+B+C+D$$.

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