Lösung.

Es wird

$ \mbox{$\displaystyle \begin{array}{rcl} \sum_{m = 2}^\infty (\zeta(m) - 1) & ... ... = 2}^\infty ((n-1)^{-1} - n^{-1}) \vspace*{1mm}\\ & = & 1 \; . \end{array}$}$