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

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

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taylor 3/(1+3x)

taylor

\frac{3}{1 + 3 x}

3 - 9 x + 27 x^{2} - 81 x^{3} + 243 x^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 3 + \frac{- 9}{1 !} x + \frac{54}{2 !} x^{2} + \frac{- 486}{3 !} x^{3} + \frac{5832}{4 !} x^{4} + \dots

Refine

= 3 - 9 x + 27 x^{2} - 81 x^{3} + 243 x^{4} + \dots

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