maclaurin ln((1+x)/(1-x))

Lösung

maclaurin

ln (\frac{1 + x}{1 - x})

2 x + \frac{2}{3} x^{3} + \frac{2}{5} x^{5} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

= 0 + \frac{\frac{d}{d x} ( ln ( \frac{1 + x}{1 - x} ) ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ln ( \frac{1 + x}{1 - x} ) ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ln ( \frac{1 + x}{1 - x} ) ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{2}{1 !} x + \frac{0}{2 !} x^{2} + \frac{4}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{48}{5 !} x^{5} + \dots

Fasse zusammen

= 2 x + \frac{2}{3} x^{3} + \frac{2}{5} x^{5} + \dots