Trigamma summation

Calculus Level 5

$\large \sum _{ n=1 }^{ \infty }{ \dfrac { { \psi }_{ 1 }( n ) }{ { 2 }^{ n-1 } } } =\dfrac { { \pi }^{ A } }{ B } +{ ( \ln { C } ) }^{ D }$

The above equation holds true for positive integers $$A,B, C$$ and $$D$$. Find $$A+B+C+D$$.

Notation: $$\psi_1 (\cdot)$$ denotes the $$1^\text{st}$$ derivative of the Digamma function.

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