maclaurin f(x)= 1/((1-x)^2)

Lösung

maclaurin

f (x) = \frac{1}{( 1 - x ) ^{2}}

1 + 2 x + 3 x^{2} + 4 x^{3} + 5 x^{4} + \dots

Schritte zur Lösung

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{2}{1 !} x + \frac{6}{2 !} x^{2} + \frac{24}{3 !} x^{3} + \frac{120}{4 !} x^{4} + \dots

Fasse zusammen

= 1 + 2 x + 3 x^{2} + 4 x^{3} + 5 x^{4} + \dots