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Vraagstuk XXXVII (Lösung von S. C. van Veen). (Dutch) JFM 47.0212.07

Für \(| z| < 1\) gilt \[ \sum_{n =1}^\infty \frac{z^n}{1-z^n} = \sum_{n =1}^\infty \frac {(-1)^{n-1}z^{ \frac{n(n +1)}2} }{(1-z)(1-z^2)(1-z^3)\cdots(1-z^{n-1})(1-z^n)^2}. \]