What is taylor (1+x)^{-3} ?

The answer to taylor (1+x)^{-3} is 1-3x+6x^2-10x^3+15x^4+\ldots

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

taylor (1+x)^{-3}

taylor

(1 + x)^{- 3}

1 - 3 x + 6 x^{2} - 10 x^{3} + 15 x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- 3}{1 !} x + \frac{12}{2 !} x^{2} + \frac{- 60}{3 !} x^{3} + \frac{360}{4 !} x^{4} + \dots

Refine

= 1 - 3 x + 6 x^{2} - 10 x^{3} + 15 x^{4} + \dots

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

\int (12 x^{2} - 8 x + 5) d x

\int 7 t d t

\frac{\partial}{\partial y} (x^{2} - x y + 5 y^{2})

\int sin (7 π t) d t

What is taylor (1+x)^{-3} ?
The answer to taylor (1+x)^{-3} is 1-3x+6x^2-10x^3+15x^4+\ldots