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 \(A+B+C+D\).

×

Problem Loading...

Note Loading...

Set Loading...