maclaurin 1/(1-2x)

Lösung

maclaurin

\frac{1}{1 - 2 x}

1 + 2 x + 4 x^{2} + 8 x^{3} + 16 x^{4} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{2}{1 !} x + \frac{8}{2 !} x^{2} + \frac{48}{3 !} x^{3} + \frac{384}{4 !} x^{4} + \dots

Fasse zusammen

= 1 + 2 x + 4 x^{2} + 8 x^{3} + 16 x^{4} + \dots

(sin (x) + x cos (x))^{^{'}}

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\int - 6 e^{- 6 x} d x