Answer by Markus Scheuer for Is this formula correct, series and Bernoulli...
Note, the generating function for the Bernoulli numbers is defined as \begin{align*} \frac{x}{e^x-1}=\sum_{n=0}^\infty\frac{B_nx^n}{n!} \end{align*} with $\frac{B_\color{blue}{n}}{n!}$ the coefficient...
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According to this page: https://proofwiki.org/wiki/Definition:Bernoulli_Numbers The series is : $\dfrac{x}{e^x-1}=1-\dfrac{x}{2}+\dfrac{B_1x^2}{2!}+\dfrac{B_2x^4}{4!}+\dfrac{B_3x^6}{6!}...$ where...
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