The aim of this note is to provide a simple proof of some well-known identities and recurrences relating classical Bernoulli and Euler numbers by using the Abel sum of the divergent series $\sum_{n=0}^\infty (-1)^{n} (n+1)^k$, $k$ a positive integers. Special attention is placed on the fact that the numerical value of these sums is determined by the linearity of the summation method involved.
Certain identities, connection and explicit formulas for the Bernoulli, Euler numbers and Riemann zeta -values
Some results associated with Bernoulli and Euler numbers with applications
A simple proof of the $A_2$ conjecture
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