What's gamma doing inside?

Calculus Level 5

k=1(1)kkΓ(k+1)[(2k+12)!]\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

CπA/BlnD, \dfrac C{\pi^{A/B} } \ln D,

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

×

Problem Loading...

Note Loading...

Set Loading...