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Popular Calculus >

taylor 1/(1-x^5)

Solution

taylor

\frac{1}{1 - x ^{5}}

Solution

1 + x^{5} + x^{10} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( \frac{1}{1 - x ^{5}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{1 - x ^{5}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{1 - x ^{5}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{0}{1 !} x + \frac{0}{2 !} x^{2} + \frac{0}{3 !} x^{3} + \frac{0}{4 !} x^{4} + \frac{120}{5 !} x^{5} + \frac{0}{6 !} x^{6} + \frac{0}{7 !} x^{7} + \frac{0}{8 !} x^{8} + \frac{0}{9 !} x^{9} + \frac{3628800}{10 !} x^{10} + \dots

Refine

= 1 + x^{5} + x^{10} + \dots

Popular Examples

integral from 0 to 1 of (29)/(x^5)

integral of (x^2-4)/(x^3-12x+3)

integral of 7^{x+2}

derivative of (x^2-100/(x-10))

derivative of sqrt(9x^2+5)

Frequently Asked Questions (FAQ)

What is taylor 1/(1-x^5) ?
The answer to taylor 1/(1-x^5) is 1+x^5+x^{10}+\ldots