What is taylor (1+x/2)^{-4} ?

The answer to taylor (1+x/2)^{-4} is 1-2x+5/2 x^2-5/2 x^3+35/16 x^4+\ldots

taylor (1+x/2)^{-4}

taylor

(1 + \frac{x}{2})^{- 4}

1 - 2 x + \frac{5}{2} x^{2} - \frac{5}{2} x^{3} + \frac{35}{16} x^{4} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( ( 1 + \frac{x}{2} ) ^{- 4} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( 1 + \frac{x}{2} ) ^{- 4} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( 1 + \frac{x}{2} ) ^{- 4} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{- 2}{1 !} x + \frac{5}{2 !} x^{2} + \frac{- 15}{3 !} x^{3} + \frac{\frac{105}{2}}{4 !} x^{4} + \dots

Refine

= 1 - 2 x + \frac{5}{2} x^{2} - \frac{5}{2} x^{3} + \frac{35}{16} x^{4} + \dots

3 x^{2} y^{^{''}} + 7 x y^{^{'}} + y = 24 x + 2

\frac{d}{d x} (\frac{x - 11}{x - 11})

\int \frac{1}{1 + 2 e ^{x} - e ^{- x}} d x

d er i v a t i v e (3 x + 5)^{7}

y^{^{'}} - \frac{y}{( 100 + 4 t )} = 150

What is taylor (1+x/2)^{-4} ?
The answer to taylor (1+x/2)^{-4} is 1-2x+5/2 x^2-5/2 x^3+35/16 x^4+\ldots