Aperiodic Alternate Divergent Series of Rational Numbers

List of sums of aperiodic alternate divergent series of rational numbers (where not all terms are integers).

$\Gamma(\,)$ denotes the Gamma function;
$\zeta(\,)$ denotes the Riemann zeta function;
$\beta(\,)$ denotes the Dirichlet beta function;
$\psi_0(\,)$ denotes the digamma function;
$\psi_1(\,)$ denotes the trigamma function.

$H_n$ denotes the n-th harmonic number
$H_{n,r}$ denotes the n-th generalized harmonic number of order r
$H_n^{(r)}$ denotes the n-th hyperharmonic number of order r

$e \approx 2.718281828459045235360287471352662497757247093699959574\ldots$ denotes the Euler constant;
$\gamma \equiv \zeta(1) \approx 0.5772156649015328606065120900824024310\ldots$ denotes the Euler-Mascheroni constant;
$A \approx 1.2824271291006226368753425688697917277676889\ldots$ denotes the Glaisher-Kinkelin constant;
$C \approx 0.9159655941772190150546035149323841107741493742816721\ldots$ denotes the Catalan constant.

GENERA

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