maclaurin ((2+x))/(1-x)

Lösung

maclaurin

\frac{( 2 + x )}{1 - x}

2 + 3 x + 3 x^{2} + 3 x^{3} + 3 x^{4} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 2 + \frac{3}{1 !} x + \frac{6}{2 !} x^{2} + \frac{18}{3 !} x^{3} + \frac{72}{4 !} x^{4} + \dots

Fasse zusammen

= 2 + 3 x + 3 x^{2} + 3 x^{3} + 3 x^{4} + \dots

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