# Who's up to the challenge? 40

**Calculus**Level 5

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

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

**Notations**:

- \(\zeta(\cdot) \) denotes the Riemann zeta function.
- \(\gamma \approx 0.5772 \), the Euler-Mascheroni constant.
- \(A\) denotes the Glaisher–Kinkelin constant.