What is taylor 1/((1-x)^3),0 ?

The answer to taylor 1/((1-x)^3),0 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/((1-x)^3),0

taylor

\frac{1}{( 1 - x ) ^{3}}, 0

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

e^{9}

\int 3 x + 2 y d y

y^{^{''}} - 8 y^{^{'}} = 64 t, y (0) = 8, y^{^{'}} (0) = 0

\int \frac{x ^{3}}{2 x + 1} d x

What is taylor 1/((1-x)^3),0 ?
The answer to taylor 1/((1-x)^3),0 is 1+3x+6x^2+10x^3+15x^4+\ldots