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

The answer to taylor 1/(3+5x) is 1/3-5/9 x+25/27 x^2-125/81 x^3+625/243 x^4+\ldots

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taylor 1/(3+5x)

taylor

\frac{1}{3 + 5 x}

\frac{1}{3} - \frac{5}{9} x + \frac{25}{27} x^{2} - \frac{125}{81} x^{3} + \frac{625}{243} x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= \frac{1}{3} + \frac{- \frac{5}{9}}{1 !} x + \frac{\frac{50}{27}}{2 !} x^{2} + \frac{- \frac{250}{27}}{3 !} x^{3} + \frac{\frac{5000}{81}}{4 !} x^{4} + \dots

Refine

= \frac{1}{3} - \frac{5}{9} x + \frac{25}{27} x^{2} - \frac{125}{81} x^{3} + \frac{625}{243} x^{4} + \dots

y = x^{\frac{5}{2}} e^{x}

f (x) = \frac{ln ( x )}{2 x}

\int x^{5} x^{3} + 6 d x

\frac{\partial}{\partial x} (yz - x w)

What is taylor 1/(3+5x) ?
The answer to taylor 1/(3+5x) is 1/3-5/9 x+25/27 x^2-125/81 x^3+625/243 x^4+\ldots