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Calculus Level 5

\[ \large \displaystyle\sum _{ n=1 }^{ \infty }{ { (-1) }^{ n }\left( { H }_{ n }-\ln { n } -\gamma \right) } =\dfrac { a\gamma -b\ln { (c\pi) } }{ 2 } \]

The equation above holds true for positive integers \(a,b\) and \(c\). Find \(a+b+c\).

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