What is maclaurin 1/(1+x^3) ?

The answer to maclaurin 1/(1+x^3) is 1-x^3+x^6-x^9+\ldots

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

maclaurin 1/(1+x^3)

maclaurin

\frac{1}{1 + x ^{3}}

1 - x^{3} + x^{6} - x^{9} + \dots

Solution steps

Apply the Maclaurin 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{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{- 6}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{0}{5 !} x^{5} + \frac{720}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{- 362880}{9 !} x^{9} + \frac{0}{10 !} x^{10} + \dots

Refine

= 1 - x^{3} + x^{6} - x^{9} + \dots

What is maclaurin 1/(1+x^3) ?
The answer to maclaurin 1/(1+x^3) is 1-x^3+x^6-x^9+\ldots