In mathematics, the Mercator series or Newton–Mercator series is the Taylor series for the natural logarithm: ln ⁡ = x − x 2 2 + x 3 3 − x 4 4 + ⋯ {\displaystyle \ln=x-{\frac {x^{2}}{2}}+{\frac {x^{3}}{3}}-{\frac {x^{4}}{4}}+\cdots } In summation notation, ln ⁡ = ∑ n = 1 ∞ n + 1 n x n. Wikipedia