Evaluate the infinite sum S=∑n=2∞(ζ(n)−1)S = \sum_{n=2}^{\infty} (\zeta(n) - 1)S=∑n=2∞(ζ(n)−1), where ζ(s)=∑k=1∞1ks\zeta(s) = \sum_{k=1}^{\infty} \frac{1}{k^s}ζ(s)=∑k=1∞ks1 is the Riemann Zeta function.
111
γ\gammaγ (the Euler-Mascheroni constant)
ln2\ln 2ln2
π26−1\frac{\pi^2}{6} - 16π2−1