What is maclaurin e^x*(1/(1-x)) ?

The answer to maclaurin e^x*(1/(1-x)) is 1+2x+5/2 x^2+8/3 x^3+65/24 x^4+\ldots

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maclaurin e^x*(1/(1-x))

maclaurin

e^{x} \cdot (\frac{1}{1 - x})

1 + 2 x + \frac{5}{2} x^{2} + \frac{8}{3} x^{3} + \frac{65}{24} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

= 1 + \frac{2}{1 !} x + \frac{5}{2 !} x^{2} + \frac{16}{3 !} x^{3} + \frac{65}{4 !} x^{4} + \dots

Refine

= 1 + 2 x + \frac{5}{2} x^{2} + \frac{8}{3} x^{3} + \frac{65}{24} x^{4} + \dots

\int e^{x^{4}} d x

n = 3 \sum \infty (\frac{2}{11})^{- n}

x^{5} cos (x)

\frac{d}{d x} (\frac{x ^{2} - 1}{x + 3})

\int \frac{1}{25 - x ^{2}} d x

What is maclaurin e^x*(1/(1-x)) ?
The answer to maclaurin e^x*(1/(1-x)) is 1+2x+5/2 x^2+8/3 x^3+65/24 x^4+\ldots