The alternating harmonic series is the series
which is the special case 
of the Dirichlet
eta function 
and also the 
case of the Mercator series.
See also
Dirichlet Eta Function, Harmonic Series, Mercator Series, Natural Logarithm of 2
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References
Havil, J. Gamma: Exploring Euler's Constant. Princeton, NJ: Princeton University Press, p. 33, 2003.
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Cite this as:
Weisstein, Eric W. "Alternating Harmonic Series." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AlternatingHarmonicSeries.html