What is taylor 1/((x+1)^2)1 ?

The answer to taylor 1/((x+1)^2)1 is 1-2x+3x^2-4x^3+5x^4+\ldots

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taylor 1/((x+1)^2)1

taylor

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

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

Solution steps

Apply the Taylor Formula

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

Refine

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

\int x^{2} 9 + x^{2} d x

\frac{1}{2002 s ^{2} + 9}

y^{^{'}} = \frac{x ^{3} y ^{3} + 4 x ^{3}}{y ^{2}}

\frac{d}{d x} (x^{2} + y^{2}) = 25

\frac{\partial}{\partial x} (9 x^{2})

What is taylor 1/((x+1)^2)1 ?
The answer to taylor 1/((x+1)^2)1 is 1-2x+3x^2-4x^3+5x^4+\ldots