Newton-Mercator series

The Mercator series, also called the Newton-Mercator series, is the Taylor series for the natural logarithm ln(1 + x) | = | sum_(k = 1)^∞ (-1)^(k + 1)/k x^k | = | x - 1/2 x^2 + 1/3 x^3 - ... for -1

alternating harmonic series | Dirichlet eta function | logarithmic number | natural logarithm