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Alternating Harmonic Series


The alternating harmonic series is the series

 sum_(k=1)^infty((-1)^(k-1))/k=ln2,

which is the special case eta(1) of the Dirichlet eta function eta(z) and also the x=1 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.

Referenced on Wolfram|Alpha

Alternating Harmonic Series

Cite this as:

Weisstein, Eric W. "Alternating Harmonic Series." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AlternatingHarmonicSeries.html

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