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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

taylor

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

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}{( 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

Refine

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

\int \frac{3 cos ( ln ( x ) )}{x} d x

\frac{d}{d x} (arctan (4^{x}))

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

6 x + 1

\int \frac{( - 2 cos ( x ) )}{sin ^{2} ( x )} d x

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