What is taylor 1/(3x+5) ?

The answer to taylor 1/(3x+5) is 1/5-3/25 x+9/125 x^2-27/625 x^3+81/3125 x^4+\ldots

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taylor 1/(3x+5)

taylor

\frac{1}{3 x + 5}

\frac{1}{5} - \frac{3}{25} x + \frac{9}{125} x^{2} - \frac{27}{625} x^{3} + \frac{81}{3125} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= \frac{1}{5} + \frac{- \frac{3}{25}}{1 !} x + \frac{\frac{18}{125}}{2 !} x^{2} + \frac{- \frac{162}{625}}{3 !} x^{3} + \frac{\frac{1944}{3125}}{4 !} x^{4} + \dots

Refine

= \frac{1}{5} - \frac{3}{25} x + \frac{9}{125} x^{2} - \frac{27}{625} x^{3} + \frac{81}{3125} x^{4} + \dots

What is taylor 1/(3x+5) ?
The answer to taylor 1/(3x+5) is 1/5-3/25 x+9/125 x^2-27/625 x^3+81/3125 x^4+\ldots