What is taylor 1/(2+7x) ?

The answer to taylor 1/(2+7x) is 1/2-7/4 x+49/8 x^2-343/16 x^3+2401/32 x^4+\ldots

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taylor 1/(2+7x)

taylor

\frac{1}{2 + 7 x}

\frac{1}{2} - \frac{7}{4} x + \frac{49}{8} x^{2} - \frac{343}{16} x^{3} + \frac{2401}{32} x^{4} + \dots

Solution steps

Apply the Taylor Formula

= \frac{1}{2} + \frac{\frac{d}{d x} ( \frac{1}{2 + 7 x} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{2 + 7 x} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{2 + 7 x} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= \frac{1}{2} + \frac{- \frac{7}{4}}{1 !} x + \frac{\frac{49}{4}}{2 !} x^{2} + \frac{- \frac{1029}{8}}{3 !} x^{3} + \frac{\frac{7203}{4}}{4 !} x^{4} + \dots

Refine

= \frac{1}{2} - \frac{7}{4} x + \frac{49}{8} x^{2} - \frac{343}{16} x^{3} + \frac{2401}{32} x^{4} + \dots

What is taylor 1/(2+7x) ?
The answer to taylor 1/(2+7x) is 1/2-7/4 x+49/8 x^2-343/16 x^3+2401/32 x^4+\ldots