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.
Alternating Harmonic Series
See also
Dirichlet Eta Function, Harmonic Series, Mercator Series, Natural Logarithm of 2Explore with Wolfram|Alpha
References
Havil, J. Gamma: Exploring Euler's Constant. Princeton, NJ: Princeton University Press, p. 33, 2003.Referenced on Wolfram|Alpha
Alternating Harmonic SeriesCite this as:
Weisstein, Eric W. "Alternating Harmonic Series." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AlternatingHarmonicSeries.html